Uma Classe de Modelos de Regressão Bivariados para Respostas Discreta e Contínua

❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❊①❛t❛s ❡ ❞❡ ❚❡❝♥♦❧♦❣✐❛

❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛

❯♠❛ ❈❧❛ss❡ ❞❡ ▼♦❞❡❧♦s ❞❡ ❘❡❣r❡ssã♦ ❇✐✈❛r✐❛❞♦s

♣❛r❛ ❘❡s♣♦st❛s ❉✐s❝r❡t❛ ❡ ❈♦♥tí♥✉❛

❲✐❧❧✐❛♥ ▲✉ís ❞❡ ❖❧✐✈❡✐r❛

❲✐❧❧✐❛♥ ▲✉ís ❞❡ ❖❧✐✈❡✐r❛

❯♠❛ ❈❧❛ss❡ ❞❡ ▼♦❞❡❧♦s ❞❡ ❘❡❣r❡ssã♦ ❇✐✈❛r✐❛❞♦s

♣❛r❛ ❘❡s♣♦st❛s ❉✐s❝r❡t❛ ❡ ❈♦♥tí♥✉❛

❚❡s❡ ❛♣r❡s❡♥t❛❞❛ ❛♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛tíst✐❝❛ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s ✲ ❉❊s✴❯❋❙❈❛r ❝♦♠♦ ♣❛rt❡ ❞♦s r❡q✉✐s✐t♦s ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ tít✉❧♦ ❞❡ ❞♦✉t♦r ❡♠ ❊st❛tíst✐❝❛✳

❖r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❈❛r❧♦s ❆❧❜❡rt♦ ❘✐❜❡✐r♦ ❉✐♥✐③

Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária UFSCar Processamento Técnico

com os dados fornecidos pelo(a) autor(a)

O48c

Oliveira, Willian Luís de

Uma classe de modelos de regressão bivariados para respostas discreta e contínua / Willian Luís de Oliveira. -- São Carlos : UFSCar, 2016.

139 p.

Tese (Doutorado) -- Universidade Federal de São Carlos, 2016.

❆❣r❛❞❡❝✐♠❡♥t♦s

❆❣r❛❞❡ç♦ ❛ ❉❡✉s ♣♦r ♠❡ ❞❛r s❛ú❞❡ ❡ s❛❜❡❞♦r✐❛✳

❆♦s ♠❡✉s ♣❛✐s ■❞❡♠❛r ❡ ❈❧❡✉s❛ q✉❡ s❡♠♣r❡ ♠❡ ❛♣♦✐❛r❛♠ ❡ ✐♥❝❡♥t✐✈❛r❛♠✳ ➚ ❆❧✐♥❡ ❈❛♠♣♦s ♣❡❧❛ ♠♦t✐✈❛çã♦✱ ❛❥✉❞❛ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳

➚ ♠✐♥❤❛ t✐❛ ▼❛r✐❛ ♣❡❧♦ ❝❛r✐♥❤♦✳

❆♦ ♠❡✉ ✐r♠ã♦ ❲❛♥❞❡r✱ ♠✐♥❤❛ s♦❜r✐♥❤❛ ❚❛✐♥❛r❛ ❡ à ▼❛r❧✐ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❞✐str❛çã♦✳ ❆♦ ♠❡✉ ♦r✐❡♥t❛❞♦r Pr♦❢✳ ❈❛r❧♦s ❆❧❜❡rt♦ ❘✐❜❡✐r♦ ❉✐♥✐③ ♣❡❧❛ ❝♦♥✜❛♥ç❛✱ ♣❛❝✐ê♥❝✐❛ ❡ ❡♥s✐♥❛♠❡♥t♦s✳

❆♦s ♣r♦❢❡ss♦r❡s ❊♥r✐❝♦ ❈♦❧♦s✐♠♦✱ ❏✉❧✐❛♥❛ ❈♦❜r❡✱ ▼ár✐♦ ❞❡ ❈❛str♦ ❡ ❘♦s❡❧✐ ▲❡❛♥❞r♦✱ ♠❡♠❜r♦s ❞❛ ❜❛♥❝❛ ❡①❛♠✐♥❛❞♦r❛✱ ♣❡❧❛s ❝♦♥tr✐❜✉✐çõ❡s ❞❛❞❛s✳

➚ ♣r♦❢❡ss♦r❛ ▼❛r✐❛ ❉✉r❜á♥✱ ♣❡❧❛ ❛❥✉❞❛ ❡ ❡♥s✐♥❛♠❡♥t♦s✳

❆♦s ♠❡✉s ❛♠✐❣♦s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ♣❡❧♦s ♠♦♠❡♥t♦s ❞❡ ❡st✉❞♦ ❡ ❞✐✈❡rsã♦✳ ❆♦s ♣r♦❢❡ss♦r❡s ❞♦ ■❈▼❈✲❯❙P ❡ ❉❊s✲❯❋❙❈❛r ♣❡❧❛ ❛t❡♥çã♦ ❞❛❞❛✳

❆♦s ❢✉♥❝✐♦♥ár✐♦s ❞♦ ❉❊s✲❯❋❙❈❛r✱ ❡♠ ❡s♣❡❝✐❛❧ à s❡❝r❡tár✐❛ ■s❛❜❡❧ ❆r❛✉❥♦ ♣♦r t♦❞❛ ❛❥✉❞❛✳

❘❡s✉♠♦

◆❡st❛ t❡s❡ é ♣r♦♣♦st❛ ✉♠❛ ❝❧❛ss❡ ❛♠♣❧❛ ❡ ❣❡r❛❧ ❞❡ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ♣❛r❛ r❡s♣♦s✲ t❛s ♠✐st❛s ❡♠ q✉❡ ❛s ❞✐str✐❜✉✐çõ❡s ❝♦♥❥✉♥t❛s sã♦ ❝♦♥str✉í❞❛s ♣❡❧♦ ♠ét♦❞♦ ❞❛ ❢❛t♦r❛çã♦ ✭❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡✱ ✭❢❞♣✮✱ ❝♦♠♦ ♦ ♣r♦❞✉t♦ ❞❡ ✉♠❛ ❢❞♣ ♠❛r❣✐♥❛❧ ❡ ✉♠❛ ❢❞♣ ❝♦♥❞✐❝✐♦♥❛❧✮✳ ➱ ❛ss✉♠✐❞♦ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❛ ❞✐str✐✲ ❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ ❞❛❞❛ ❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ ♣❡rt❡♥❝❡♠ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ❞❡ ❞✐str✐❜✉✐çõ❡s ✉♥✐♣❛r❛♠étr✐❝❛ ♦✉ ❜✐♣❛r❛♠étr✐❝❛✳ ❆❧é♠ ❞✐ss♦✱ ❛s ♠é❞✐❛s ♠❛r❣✐♥❛✐s sã♦ r❡❧❛❝✐♦♥❛❞❛s ❛ ❝♦✈❛r✐á✈❡✐s ❛tr❛✈és ❞❡ ❢✉♥çõ❡s ❞❡ ❧✐❣❛çã♦ ✉s❛♥❞♦ ♣r❡❞✐t♦r❡s ❧✐♥❡❛r ❡✴♦✉ ♥ã♦ ❧✐♥❡❛r ❡✴♦✉ ♥ã♦ ♣❛r❛♠étr✐❝♦ ❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s r❡s♣♦st❛s é ✐♥s❡r✐❞❛ ♥♦ ♠♦❞❡❧♦ ✈✐❛ ❛ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧✳ ▼ét♦❞♦s ❞❡ ❡st✐♠❛✲ çã♦✱ ❛♥á❧✐s❡s ❞❡ ❞✐❛❣♥óst✐❝♦ ❡ té❝♥✐❝❛s ❞❡ ✐♥✢✉ê♥❝✐❛ sã♦ ❛♣r❡s❡♥t❛❞❛s ❛ss✐♠ ❝♦♠♦ ✉♠ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♠♦❞❡❧♦s ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧ ❡ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦✱ ❞♦✐s ❝❛s♦s ♣❛rt✐❝✉❧❛r❡s ❞❛ ❝❧❛ss❡ ♣r♦♣♦st❛✳ ❋✐♥❛❧♠❡♥t❡✱ ✉♠ ❞♦s ♠♦✲ ❞❡❧♦s ♣r♦♣♦st♦s é ✉s❛❞♦ ❡♠ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s r❡❛✐s ❡♥✈♦❧✈❡♥❞♦ ❣❛st♦s t♦t❛✐s ❝♦♠ ❝✉✐❞❛❞♦s ♣❛r❛ ❝❛❞❛ ♣❛❝✐❡♥t❡ ❞✉r❛♥t❡ ❛ ❤♦s♣✐t❛❧✐③❛çã♦✱ ♦ ✉s♦ ♦✉ ♥ã♦ ❞❛ ✉♥✐❞❛❞❡ ❞❡ tr❛t❛♠❡♥t♦ ✐♥t❡♥s✐✈♦ ❡ ❛ ✐❞❛❞❡ ❞♦ ♣❛❝✐❡♥t❡✳

P❛❧❛✈r❛s✲❝❤❛✈❡✿ ▼♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜✐✈❛r✐❛❞♦s✳ ❘❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✳ ▼ét♦❞♦ ❞❛ ❢❛t♦r❛çã♦✳ ❉❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ r❡s♣♦st❛s✳

❆❜str❛❝t

■♥ t❤✐s t❤❡s✐s✱ ❛ ✇✐❞❡ ❣❡♥❡r❛❧ ❝❧❛ss ♦❢ ♠♦❞❡❧s ❢♦r ♠✐①❡❞ r❡s♣♦♥s❡s ✐s ♣r♦♣♦s❡❞ ✐♥ ✇❤✐❝❤ ❥♦✐♥t ❞✐str✐❜✉t✐♦♥s ❛r❡ ❝♦♥str✉❝t❡❞ ❜② t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❛♣♣r♦❛❝❤ ✭♣r♦❜❛❜✐❧✐t② ❞❡♥✲ s✐t② ❢✉♥❝t✐♦♥s✱ ✭♣❞❢✮✱ ❛s t❤❡ ♣r♦❞✉❝t ♦❢ ❛ ♠❛r❣✐♥❛❧ ♣❞❢ ❛♥❞ ❛ ❝♦♥❞✐t✐♦♥❛❧ ♣❞❢✮✳ ■t ✐s ❛ss✉♠❡❞ t❤❛t t❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❞✐s❝r❡t❡ r❡s♣♦♥s❡ ❛♥❞ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ❞✐str✐❜✉t✐♦♥ ♦❢ t❤❡ ❝♦♥t✐♥✉♦✉s r❡s♣♦♥s❡ ❣✐✈❡♥ t❤❡ ❞✐s❝r❡t❡ ✈❛r✐❛❜❧❡ ❜❡❧♦♥❣ t♦ ♦♥❡✲ ♦r t✇♦✲♣❛r❛♠❡t❡r ❡①♣♦♥❡♥t✐❛❧ ❢❛♠✐❧② ♦❢ ❞✐str✐❜✉t✐♦♥s✳ ❋✉rt❤❡r♠♦r❡✱ t❤❡ ♠❛r❣✐♥❛❧ ♠❡❛♥s ❛r❡ r❡❧❛t❡❞ t♦ t❤❡ ❝♦✈❛r✐❛t❡s ❜② ❧✐♥❦ ❢✉♥❝t✐♦♥s ✉s✐♥❣ ❧✐♥❡❛r ❛♥❞✴♦r ♥♦♥❧✐♥❡❛r ❛♥❞✴♦r ♥♦♥✲♣❛r❛♠❡tr✐❝ ♣r❡✲ ❞✐❝t♦rs ❛♥❞ ❛ ❞❡♣❡♥❞❡♥❝② str✉❝t✉r❡ ❜❡t✇❡❡♥ t❤❡ r❡s♣♦♥s❡s ✐s ✐♥tr♦❞✉❝❡❞ ✐♥t♦ t❤❡ ♠♦❞❡❧ ✈✐❛ t❤❡ ❝♦♥❞✐t✐♦♥❛❧ ♠❡❛♥✳ ❊st✐♠❛t✐♦♥ ♠❡t❤♦❞s✱ ❞✐❛❣♥♦st✐❝ ❛♥❛❧②s✐s ❛♥❞ ✐♥✢✉❡♥❝❡ t❡❝❤✲ ♥✐q✉❡s ❛r❡ ♣r❡s❡♥t❡❞ ❛s ✇❡❧❧ ❛s ❛ s✐♠✉❧❛t✐♦♥ st✉❞② ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥t✐❛❧ ❛♥❞ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠❡tr✐❝ ♠♦❞❡❧s✱ t✇♦ ♣❛rt✐❝✉❧❛r ❝❛s❡s ♦❢ t❤❡ ♣r♦♣♦s❡❞ ❝❧❛ss✳ ❋✐♥❛❧❧②✱ ♦♥❡ ♦❢ t❤❡ ♣r♦♣♦s❡❞ ♠♦❞❡❧s ✐s ✉s❡❞ ✐♥ ❛ r❡❛❧ ❞❛t❛ s❡t ✐♥✈♦❧✈✐♥❣ t❤❡ t♦t❛❧ ❝♦st ♦❢ ❝❛r❡ ❢♦r ❡❛❝❤ ♣❛t✐❡♥t ❞✉r✐♥❣ ❤♦s♣✐t❛❧✐③❛t✐♦♥✱ t❤❡ ✉s❡ ♦r ♥♦t ♦❢ t❤❡ ✐♥t❡♥s✐✈❡ tr❡❛t♠❡♥t ✉♥✐ts ❛♥❞ t❤❡ ❛❣❡ ♦❢ t❤❡ ♣❛t✐❡♥t✳

❑❡②✇♦r❞s✿ ❇✐✈❛r✐❛t❡ r❡❣r❡ss✐♦♥ ♠♦❞❡❧s✳ ❉✐s❝r❡t❡ ❛♥❞ ❝♦♥t✐♥✉♦✉s r❡s♣♦♥s❡s✳ ❈♦♥✲ ❞✐t✐♦♥❛❧ ❛♣♣r♦❛❝❤✳ ❉❡♣❡♥❞❡♥❝② ❜❡t✇❡❡♥ t❤❡ r❡s♣♦♥s❡s✳

❙✉♠ár✐♦

❘❡s✉♠♦ ✐

❆❜str❛❝t ✐✐

✶ ■♥tr♦❞✉çã♦ ✶

✶✳✶ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷ ❆♣r❡s❡♥t❛çã♦ ❞♦s ❝❛♣ít✉❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾

✷ ▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ♠✐st♦s ✶✷

✷✳✶ ▼♦❞❡❧♦ ♣❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✶✳✶ ▼á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼ ✷✳✶✳✷ ■♥t❡r✈❛❧♦s ❞❡ ❝♦♥✜❛♥ç❛ ❛ss✐♥tót✐❝♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✷✳✶✳✸ ❚❡st❡ ❞❡ ❤✐♣ót❡s❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✷✳✷ ▼♦❞❡❧♦ s❡♠✐♣❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹ ✷✳✷✳✶ ❊s❝♦r❡ ❧♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹

✸ ▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s s❡♠✐♣❛r❛♠étr✐❝♦s ✷✽

✐✈ ✸✳✶ P✲s♣❧✐♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽ ✸✳✶✳✶ ❇❛s❡ ❇✲s♣❧✐♥❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾ ✸✳✶✳✷ ▼❛tr✐③ ❞❡ ♣❡♥❛❧✐③❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✸✳✶✳✸ ❆♣❧✐❝❛çã♦ ❞❛ té❝♥✐❝❛ P✲s♣❧✐♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✸✳✷ ▼♦❞❡❧♦s ❛❞✐t✐✈♦s ❣❡♥❡r❛❧✐③❛❞♦s ❝♦♠ P✲s♣❧✐♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✸✳✷✳✶ ❚r❛♥s❢♦r♠❛çã♦ ❞❛ ❜❛s❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✸✳✸ ▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ P✲s♣❧✐♥❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✺

✹ ❈❛s♦s ♣❛rt✐❝✉❧❛r❡s ✺✸

✹✳✶ ▼♦❞❡❧♦ ❇❡r♥♦✉❧❧✐✲♥♦r♠❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✹✳✶✳✶ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✺ ✹✳✷ ▼♦❞❡❧♦ P♦✐ss♦♥✲♥♦r♠❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✻ ✹✳✷✳✶ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✸ ▼♦❞❡❧♦ ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✼ ✹✳✸✳✶ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✹✳✹ ▼♦❞❡❧♦ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ✹✳✹✳✶ ❊st✐♠❛çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵

✺ ❚é❝♥✐❝❛s ❞❡ ❞✐❛❣♥óst✐❝♦ ❡ ✐♥✢✉ê♥❝✐❛ ✻✷

✈

✺✳✶✳✸ ❘❡sí❞✉♦s ❝♦♠♣♦♥❡♥t❡s ❞❛ ❞❡s✈✐â♥❝✐❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✺✳✷ ■♥✢✉ê♥❝✐❛ ❧♦❝❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✼ ✺✳✸ ■♥✢✉ê♥❝✐❛ ❣❧♦❜❛❧ ♦✉ t♦t❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✶

✻ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ✼✸

✻✳✶ ▼♦❞❡❧♦ ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✻✳✷ ▼♦❞❡❧♦ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾

✼ ❆♣❧✐❝❛çã♦ ✶✶✶

✽ ❈♦♥❝❧✉sã♦ ✶✷✵

✾ Pr♦♣♦st❛s ❞❡ tr❛❜❛❧❤♦s ❢✉t✉r♦s ✶✷✸

❆ ❉❡r✐✈❛❞❛s ❞❛ ❢✉♥çã♦ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ✶✷✺

❈❛♣ít✉❧♦ ✶

■♥tr♦❞✉çã♦

❊♠ ♠✉✐t❛s ár❡❛s ❞❛ ❝✐ê♥❝✐❛✱ t❛✐s ❝♦♠♦ ❡❝♦♥♦♠✐❛✱ ♠❡❞✐❝✐♥❛ ❡ ♣s✐❝♦❧♦❣✐❛✱ sã♦ ❝♦♠✉♥s s✐t✉❛çõ❡s ❡♠ q✉❡ ❞✉❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛s ❛ss♦❝✐❛❞❛s ❝♦♠ ♦ ♠❡s♠♦ ✐♥❞✐✈í❞✉♦ sã♦ ♦❜✲ s❡r✈❛❞❛s s✐♠✉❧t❛♥❡❛♠❡♥t❡✳ P♦r ❡①❡♠♣❧♦✱ ❡♠ ✉♠ ❤♦s♣✐t❛❧ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r ♦s ❣❛st♦s ♠é❞✐♦s ❞♦s ♣❛❝✐❡♥t❡s ♥♦ ♣❡rí♦❞♦ ❞❡ ✐♥t❡r♥❛çã♦ ❡ s❡ ❡❧❡ ✉t✐❧✐③♦✉ ♦✉ ♥ã♦ ♦ ❝❡♥tr♦ ❝✐rúr✲ ❣✐❝♦ ♥❡st❡ ♣❡rí♦❞♦✳ ◆❛ ✉♥✐✈❡rs✐❞❛❞❡✱ ♣♦❞❡✲s❡ ♦❜s❡r✈❛r ❛s ♥♦t❛s ❞♦s ❛❧✉♥♦s ❡♠ ✉♠❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐s❝✐♣❧✐♥❛ ❡ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ ❢❛❧t❛s ❞♦ ❛❧✉♥♦✳ ◆❡st❡s ❝❛s♦s✱ ✉♠❛ ♣♦ssí✈❡❧ ❛♥á❧✐s❡ ♣♦❞❡r✐❛ s❡r r❡❛❧✐③❛❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❝❛❞❛ ✉♠❛ ❞❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞❡ ❢♦r♠❛ ✐♥❞❡♣❡♥❞❡♥t❡✱ ✐st♦ é✱ ❛❞♦t❛♥❞♦ ✉♠ ♠♦❞❡❧♦ ♠❛r❣✐♥❛❧ ♣❛r❛ ❝❛❞❛ ✉♠❛ ❞❛s r❡s♣♦st❛s ❝♦♥✲ s✐❞❡r❛❞❛s✳ ❊♥tr❡t❛♥t♦✱ s❡ ❛ r❡❧❛çã♦ ✐♥trí♥s❡❝❛ ❡♥tr❡ ❛s ❞✉❛s r❡s♣♦st❛s ♥ã♦ é ❝♦♥s✐❞❡r❛❞❛ ♥❛ ❛♥á❧✐s❡✱ r❡s✉❧t❛❞♦s ✐rr❡❛✐s ♣♦❞❡♠ s❡r ❣❡r❛❞♦s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s sã♦ ✈✐st♦s ❝♦♠♦ ✉♠❛ ❜♦❛ ❛❧t❡r♥❛t✐✈❛✱ ❡♠ q✉❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s r❡s♣♦st❛s é ❛❞♦t❛❞❛✳

❆ ✐♥s❡rçã♦ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ♥❛ ♠♦❞❡❧❛❣❡♠ ♠✉✐t❛s ✈❡③❡s ❛ t♦r♥❛ ♠❡❧❤♦r s❡ ❝♦♠♣❛r❛❞❛ às ❛♥á❧✐s❡s ♠❛r❣✐♥❛✐s✱ ❧❡✈❛♥❞♦ ❛ r❡s✉❧t❛❞♦s ♠❛✐s ❝♦♥✜á✈❡✐s✳ ❆ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ t❡♠ s✐❞♦ ♦❜❥❡t♦ ❞❡ ❡st✉❞♦ ❞❡ ❛❧❣✉♥s tr❛❜❛❧❤♦s ❡♥✈♦❧✈❡♥❞♦ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ✭❖❧❦✐♥ ✫ ❚❛t❡✱ ✶✾✻✶✮✳

✷

◆♦s ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❡♠ ❣❡r❛❧✱ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ♣♦❞❡♠ s❡r ❛♠❜❛s ❞✐s❝r❡t❛s✱ ❛♠❜❛s ❝♦♥tí♥✉❛s ♦✉ ✉♠❛ ❞✐s❝r❡t❛ ❡ ❛ ♦✉tr❛ ❝♦♥tí♥✉❛✳ ▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ ❛♠❜❛s ❛s r❡s♣♦st❛s ❝♦♥tí♥✉❛s tê♠ s✐❞♦ ❛♠♣❧❛♠❡♥t❡ ❡①♣❧♦r❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛ ✭❙❝♦❧❧♥✐❦✱ ✷✵✵✷❀ ❙♦♥❣ ❡t ❛❧✳✱ ✷✵✵✹✮✱ ❝♦♠ ❞❡st❛q✉❡ ♣❛r❛ r❡s♣♦st❛s s❡❣✉✐♥❞♦ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ✭♦✉ ❛♣r♦✲ ①✐♠❛❞❛♠❡♥t❡ ♥♦r♠❛❧✮✱ ❡♠ q✉❡ ✉♠❛ ❝❧❛ss❡ ❣❡r❛❧ ❛❞❡q✉❛❞❛ ❞❡ ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❡stá ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ❛ ❛♥á❧✐s❡ ❞♦s ❞❛❞♦s ✭❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞✱ ✶✾✾✺❀ ▲✐♥ ❡t ❛❧✳✱ ✷✵✶✵✮✳ ▼♦✲ ❞❡❧♦s ❜✐✈❛r✐❛❞♦s ♣❛r❛ ❞❛❞♦s ❜✐♥ár✐♦s ✭❈♦①✱ ✶✾✼✷❀ ▼❝❉♦♥❛❧❞✱ ✶✾✾✸❀ ❙❤✉❧ts ❡t ❛❧✳✱ ✷✵✵✾✮ ❡ ❞❛❞♦s ❞❡ ❝♦♥t❛❣❡♠ ✭❏✉♥❣ ✫ ❲✐♥❦❡❧♠❛♥♥✱ ✶✾✾✸❀ ✈❛♥ ❖♣❤❡♠✱ ✶✾✾✾❀ ❇❡r❦❤♦✉t ✫ P❧✉❣✱ ✷✵✵✹❀ ❑❤❛❢r✐ ❡t ❛❧✳✱ ✷✵✵✽✮ t❛♠❜é♠ tê♠ ❣❛♥❤❛❞♦ ❞❡st❛q✉❡✳ ❖ ♠❡s♠♦ ♥ã♦ ♦❝♦rr❡ q✉❛♥❞♦ ❛♠❜❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ sã♦ ❝❛t❡❣ór✐❝❛s✱ ♣♦r ❡①❡♠♣❧♦✳

✸

♣❛r❛ r❡s♣♦st❛s ♠✐st❛s ✉t✐❧✐③❛♥❞♦ ❝ó♣✉❧❛s t❛♠❜é♠ tê♠ s✐❞♦ ❡①♣❧♦r❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❡♠❜♦r❛ ❛ q✉❛♥t✐❞❛❞❡ ❞❡ tr❛❜❛❧❤♦s ❞✐s♣♦♥í✈❡✐s s❡❥❛ ♣❡q✉❡♥❛✳ P❛r❛ ♠❛✐s ❞❡t❛❧❤❡s✱ ✈✐❞❡ ❞❡ ▲❡♦♥ ✫ ❲✉ ✭✷✵✶✶✮ ❡ ❇❡✐❧❡✐ ✭✷✵✶✸✮✳

❯♠❛ ♠❛♥❡✐r❛ ♠❛✐s ❞✐r❡t❛ ♣❛r❛ ❝♦♥str✉✐r ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ♠✐st♦s✱ ❜❛st❛♥t❡ ❛♣❧✐✲ ❝❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛✱ é ❛ té❝♥✐❝❛ ❞❛ ❢❛t♦r❛çã♦ ❡♠ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛ ❞❛s r❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ é ❡s❝r✐t❛ ❝♦♠♦ ♣r♦❞✉t♦ ❡♥tr❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♠❛r❣✐♥❛❧✱ ❞❡ ✉♠❛ ❞❛s r❡s♣♦st❛s ❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧✱ ❞❛ ♦✉tr❛ r❡s♣♦st❛ ❞❛❞❛ ❛ ♣r✐♠❡✐r❛✳ ❉❡st❛ ❢♦r♠❛✱ ❞♦✐s ❞✐st✐♥t♦s ♠♦❞❡❧♦s ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞♦s✿ ♦ ♠♦❞❡❧♦ q✉❡ ❝♦♥s✐❞❡r❛ ❛ ❞✐s✲ tr✐❜✉✐çã♦ ♠❛r❣✐♥❛❧ ❞❛ r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❝♦♥❞✐❝✐♦♥❛ ❛ ✈❛r✐á✈❡❧ ❝♦♥tí♥✉❛ à ❞✐s❝r❡t❛ ❡ ♦ ♠♦❞❡❧♦ q✉❡ ❝♦♥s✐❞❡r❛ ❛ ❞❡♥s✐❞❛❞❡ ♠❛r❣✐♥❛❧ ❞❛ ✈❛r✐á✈❡❧ ❝♦♥tí♥✉❛ ❡ ❝♦♥❞✐❝✐♦♥❛ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ à ❝♦♥tí♥✉❛✳ ◆♦ ♣r✐♠❡✐r♦ ❝❛s♦✱ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ é tr❛t❛❞❛ ❝♦♠♦ r❡s♣♦st❛ ♣r✐♠ár✐❛ ❡♥q✉❛♥t♦ q✉❡ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ é ❝♦♥s✐❞❡r❛❞❛ ❛ ✈❛✲ r✐á✈❡❧ ✐♥t❡r♠❡❞✐ár✐❛✳ P❡♥s❛♠❡♥t♦ ❛♥á❧♦❣♦ é r❡❛❧✐③❛❞♦ ❛♦ s❡❣✉♥❞♦ ♠♦❞❡❧♦✳ ❆ s❡❣✉✐r✱ ❛♣r❡s❡♥t❛♠♦s ✉♠❛ r❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛ ❞♦s ♣r✐♥❝✐♣❛✐s tr❛❜❛❧❤♦s q✉❡ ✉t✐❧✐③❛♠ ❛ té❝♥✐❝❛ ❞❛ ❢❛t♦r❛çã♦✱ ❝♦♠ ❞❡st❛q✉❡ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❝♦♠ r❡s♣♦st❛s ♠✐st❛s✳

✶✳✶ ❘❡✈✐sã♦ ❜✐❜❧✐♦❣rá✜❝❛

✹

r❡s♣♦st❛s✳ ❯♠❛ ❛♥á❧✐s❡ ❜❛②❡s✐❛♥❛ ♣❛r❛ ♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦ é ❛❜♦r❞❛❞❛ t❡♥❞♦ ❝♦♠♦ ♠♦t✐✈❛çã♦ ❞❛❞♦s ❞❡ tr❛t❛♠❡♥t♦s ❝❧í♥✐❝♦s ❞❡ ❝❛s❛✐s ✐♥❢ért❡✐s✳

❚r❛❜❛❧❤♦s ❝♦♥s✐❞❡r❛♥❞♦ ❛♠❜❛s ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❝♦♥tí♥✉❛s t❛♠❜é♠ sã♦ ❡♥❝♦♥✲ tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✳ ❙❝♦❧❧♥✐❦ ✭✷✵✵✷✮ ❛♥❛❧✐s❛ ❞♦✐s ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ♠♦t✐✈❛❞♦s ♣♦r ❞❛❞♦s ❜✐✈❛r✐❛❞♦s ❞❡ s✐♥✐str♦s ❡♠ q✉❡ ❛ ❛♥á❧✐s❡ é r❡❛❧✐③❛❞❛ ❡♠ r❡❧❛çã♦ ❛ s❡❣✉r♦s ❝♦♥✲ tr❛ ❛❝✐❞❡♥t❡s✳ ❙ã♦ ♦❜s❡r✈❛❞❛s ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ✈❛❧♦r ❞❡ ♣❡r❞❛ ❡ ✈❛❧♦r ❞❡ ❞❡s♣❡s❛s ❛❧♦❝❛❞❛s ❝♦♠ ❛❥✉st❡ ❞❡ s✐♥✐str♦✳ ❊♠ ❛♠❜♦s ♦s ♠♦❞❡❧♦s✱ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ sã♦ ❝♦♥s✐✲ ❞❡r❛❞❛s ❞✐r❡t❛♠❡♥t❡ r❡❧❛❝✐♦♥❛❞❛s ✉♠❛ ❛ ♦✉tr❛✳ ❙♦♥❣ ❡t ❛❧✳ ✭✷✵✵✹✮ tê♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ♦❜❥❡t✐✈♦ ❡st✐♠❛r ❛ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❝♦♥t❛❣❡♠ ❞❡ ❝é❧✉❧❛s CD4+ ❡ ❝❛r❣❛ ✈✐r❛❧ ❞❡ ❍■❱✱ ❞❡ ✉♠❛ ♣❡sq✉✐s❛ s♦❜r❡ ❍■❱✳ ❆♠❜❛s ❛s ✈❛r✐á✈❡✐s sã♦ ❛ss✉♠✐❞❛s ♥♦r♠❛❧♠❡♥t❡ ❞✐str✐❜✉í❞❛s s❡♥❞♦ q✉❡ ❝❛r❣❛ ✈✐r❛❧ ❞❡ ❍■❱ é ❝♦♥❞✐❝✐♦♥❛❞❛ à ❝♦♥t❛❣❡♠ ❞❡ ❝é❧✉❧❛s ❞❡CD4+✳ ❖s ❞❛❞♦s sã♦ ♦❜t✐❞♦s ❞❡ ♠✉❧❤❡r❡s ❣rá✈✐❞❛s ❡ ❛ ❝♦rr❡❧❛çã♦✱ ❡st✐♠❛❞❛ ♣♦r ♠❡✐♦ ❞❡ ❡q✉❛çõ❡s ❞❡ ❡st✐♠❛çã♦ ❣❡♥❡r❛❧✐③❛❞❛s✱ ❢❛③✲s❡ ♥❡❝❡ssár✐❛ ✉♠❛ ✈❡③ q✉❡ ♦ t❡st❡ ♣❛r❛ ❝❛r❣❛ ✈✐r❛❧ ❞❡ ❍■❱ ❢♦r♥❡❝❡ ✐♥❢♦r♠❛çã♦ q✉❡ é ✉t✐❧✐③❛❞❛ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❝♦♥t❛❣❡♠ ❞❡ ❝é❧✉❧❛s CD4+✳

✺

❞✐s❝r❡t♦ ❡ s❡❣✉❡ ❞✐str✐❜✉✐çã♦ ♠✉❧t✐♥♦♠✐❛❧ ❡♥q✉❛♥t♦ q✉❡ ♦✉tr♦ ✈❡t♦r ❞❡ ✈❛r✐á✈❡✐s r❡s♣♦st❛ é ❝♦♥tí♥✉♦ ❡ s✉❛ ❞✐str✐❜✉✐çã♦✱ ❝♦♥❞✐❝✐♦♥❛❞❛ ❛♦ ✈❡t♦r ❞❡ ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞✐s❝r❡t♦✱ é ❝♦♥s✐❞❡r❛❞❛ ♥♦r♠❛❧ ♠✉❧t✐✈❛r✐❛❞❛✳ ❈♦♠♦ ❡♠ ❚❛t❡ ✭✶✾✺✹✮✱ ♦ ✐♥t❡r❡ss❡ é ❡♥❝♦♥tr❛r ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ♦s ✈❡t♦r❡s ❞❡ r❡s♣♦st❛s ❞✐s❝r❡t♦s ❡ ❝♦♥tí♥✉♦s✳ P❛r❛ ✐❧✉str❛r ♦ ♠♦❞❡❧♦ ♣r♦♣♦st♦✱ é ✉t✐❧✐③❛❞♦ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s ❝♦♥t❡♥❞♦ ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ♠❡♠❜r♦s ❞❡ ♣❛rt✐❞♦s ♣♦❧ít✐❝♦s ❜r✐tâ♥✐❝♦s✳ ▲❛✉r✐t③❡♥ ✫ ❲❡r♠✉t❤ ✭✶✾✽✾✮ ❞❡s❡♥✈♦❧✈❡♠ ✉♠❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❡st❛tíst✐❝♦s ❞❡♥♦♠✐♥❛❞❛ ♠♦❞❡❧♦s ❣rá✜❝♦s ♣❛r❛ ✈❛r✐á✈❡✐s r❡s♣♦st❛ ♠✐st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✱ ❜❛s❡❛❞❛ ♥❛ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧ ❝♦♥❞✐❝✐♦♥❛❧✳ ❊st❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s t❡♠ ❝♦♠♦ ♣r✐♥❝✐♣❛❧ ✜♥❛❧✐❞❛❞❡ ❞❡s❝r❡✈❡r ❡ ✐♥✈❡st✐❣❛r ❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛✳ ❯♠❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♣♦r ❖❧❦✐♥ ✫ ❚❛t❡ ✭✶✾✻✶✮ ♣♦❞❡ s❡r ✈✐st❛ ❡♠ ❞❡ ▲❡♦♥ ✫ ❈❛rr✐èr❡ ✭✷✵✵✼✮✳

❉✐❢❡r❡♥t❡ ❞♦s ♠♦❞❡❧♦s ❞❡ ❚❛t❡ ✭✶✾✺✹✮ ❡ ❖❧❦✐♥ ✫ ❚❛t❡ ✭✶✾✻✶✮ ❡♠ q✉❡ ♦ ❝♦♥❞✐❝✐♦♥❛✲ ♠❡♥t♦ é r❡❛❧✐③❛❞♦ ♥❛ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❈♦① ✭✶✾✼✷✮ ❝♦♥s✐❞❡r❛ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ ❞❛❞♦s ❜✐✈❛r✐❛❞♦s ♠✐st♦ ❡♠ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ é ♥♦r♠❛❧ ❡ ❛ ❞✐s✲ tr✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ✈❛r✐á✈❡❧ ❝♦♥tí♥✉❛✱ é ❇❡r♥♦✉❧❧✐✱ ❡♠ q✉❡ ❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ❧♦❣íst✐❝❛ é ❛❞♦t❛❞❛✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ ❈❛t❛❧❛♥♦ ✫ ❘②❛♥ ✭✶✾✾✷✮ ❝♦♥✲ s✐❞❡r❛♠ ✉♠ ♠♦❞❡❧♦ ❜✐✈❛r✐❛❞♦ ❝✉❥❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ t❛♠❜é♠ é ❝♦♥❞✐❝✐♦♥❛❞❛ à ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ ❡ ❛ss✉♠✐❞❛ s❡❣✉✐♥❞♦ ❞✐str✐❜✉✐çã♦ ❇❡r♥♦✉❧❧✐✳ ❆❧é♠ ❞✐ss♦✱ ✉♠❛ ✈❛r✐á✈❡❧ ❧❛t❡♥t❡ ❝♦♥tí♥✉❛ ♥ã♦ ♦❜s❡r✈❛❞❛ ❛ss♦❝✐❛❞❛ à ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ é ✐♥s❡r✐❞❛ ♥♦ ♠♦❞❡❧♦ ❛ ✜♠ ❞❡ ♦❜t❡r ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛ ❞♦ ♠♦❞❡❧♦ ❜✐✈❛r✐❛❞♦ ♠✐st♦✳ ❆s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❝♦♥tí♥✉❛ ❡ ❧❛t❡♥t❡ ♥ã♦ ♦❜s❡r✈❛❞❛ s❡❣✉❡♠ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛✲ ♠❡♥t❡ ♥♦r♠❛❧ ❜✐✈❛r✐❛❞❛✱ s❡♥❞♦ ♦ ♠♦❞❡❧♦ ♣❛r❛♠❡tr✐③❛❞♦ ❞❡ t❛❧ ❢♦r♠❛ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛ ❞❛s r❡s♣♦st❛s s❡❥❛ ❡①♣r❡ss❛ ❝♦♠♦ ✉♠ ♣r♦❞✉t♦ ❡♥tr❡ ❛ ❞✐str✐❜✉✐çã♦ ♠❛r❣✐♥❛❧ ❞❛ r❡s♣♦st❛ ❝♦♥tí♥✉❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ r❡s♣♦st❛ ❞✐s❝r❡t❛✱ ❞❛❞❛ ❛ r❡s♣♦st❛ ❝♦♥tí♥✉❛✳

✻

❧✐♥❡❛r ❡ ♣r♦❜✐t♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ s❡♥❞♦ ✉t✐❧✐③❛❞♦s ❝♦♠♦ ♠♦t✐✈❛çã♦ ❞❛❞♦s ❞❡ ✉♠ ❡st✉❞♦ ❞❡ t♦①✐❝✐❞❛❞❡ ❡♠ r❛t♦s✳ ❊♥tr❡t❛♥t♦✱ ❞♦✐s ♣r♦❜❧❡♠❛s sã♦ ❡♥❝♦♥tr❛❞♦s ♥♦s ♠♦❞❡❧♦s ❞❡ ❈♦① ✭✶✾✼✷✮ ❡ ❈❛t❛❧❛♥♦ ✫ ❘②❛♥ ✭✶✾✾✷✮✿ ♦s ♣❛râ♠❡tr♦s ❞❡ r❡❣r❡ssã♦ ♥♦s ♠♦❞❡❧♦s ❧♦❣íst✐❝♦ ✭❈♦①✱ ✶✾✼✷✮ ❡ ♣r♦❜✐t♦ ✭❈❛t❛❧❛♥♦ ✫ ❘②❛♥✱ ✶✾✾✷✮ ♥ã♦ tê♠ ✉♠❛ ✐♥t❡r♣r❡t❛çã♦ ♠❛r❣✐♥❛❧ ❡ ❛❧é♠ ❞✐ss♦✱ s✉❛s ❡st✐♠❛t✐✈❛s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ♥ã♦ sã♦ ❝♦♥s✐st❡♥t❡s q✉❛♥❞♦ ❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ ♥♦ ♠♦❞❡❧♦ ❜✐✈❛r✐❛❞♦ é ♠❛❧ ❡s♣❡❝í✜❝❛❞❛✱ ♦ q✉❡ ♥ã♦ é ♦ ✐❞❡❛❧ ❡♠ ❛❧❣✉♠❛s ❛♣❧✐❝❛çõ❡s✳ ❈♦① ✫ ❲❡r♠✉t❤ ✭✶✾✾✷✮ ❝♦♠♣❛r❛♠ ❛❧❣✉♥s ❞✐❢❡r❡♥t❡s ♠♦❞❡❧♦s ♣❛r❛ ❞❛❞♦s ❜✐✈❛r✐❛❞♦s ❞✐s❝r❡t♦ ❡ ❝♦♥tí♥✉♦✱ ❡♠ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛ é ❡①♣r❡ss❛ ❝♦♠♦ ✉♠ ♣r♦❞✉t♦ ❡♥tr❡ ✉♠❛ ❞✐str✐❜✉✐çã♦ ♠❛r❣✐♥❛❧ ❡ ✉♠❛ ❝♦♥❞✐❝✐♦♥❛❧✳ ❆❧é♠ ❞✐ss♦✱ ♦s ❛✉t♦r❡s ♥♦t❛♠ q✉❡ ❛ ✐♥t❡r♣r❡t❛çã♦ ♠❛r❣✐♥❛❧ ❞♦s ♣❛râ♠❡tr♦s ❞❡ r❡❣r❡ssã♦ é ♣♦ssí✈❡❧ s♦♠❡♥t❡ s❡ ❛ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ é r❡❧❛❝✐♦♥❛❞❛ ❛ ❝♦✈❛r✐á✈❡✐s ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ❧✐♥❡❛r✳

Pr♦❝✉r❛♥❞♦ s♦❧✉❝✐♦♥❛r ♦s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s ♥♦s ♠♦❞❡❧♦s ❞❡ ❈♦① ✭✶✾✼✷✮ ❡ ❈❛t❛✲ ❧❛♥♦ ✫ ❘②❛♥ ✭✶✾✾✷✮✱ ❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞ ✭✶✾✾✺✮ ❛♣r❡s❡♥t❛♠ ✉♠ ♠♦❞❡❧♦ ♣❛r❛ r❡s♣♦st❛s ❜✐✈❛r✐❛❞❛s ❝♦♥tí♥✉❛ ❡ ❞✐s❝r❡t❛ ❡♠ q✉❡ ♦s ♣❛râ♠❡tr♦s ❞❡ r❡❣r❡ssã♦ ❞❡ ❛♠❜❛s ❛s ✈❛r✐á✈❡✐s tê♠ ✐♥t❡r♣r❡t❛çã♦ ♠❛r❣✐♥❛❧ ❡ ♦s r❡s♣❡❝t✐✈♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ sã♦ ❝♦♥s✐st❡♥t❡s✱ ♠❡s♠♦ s❡ ❛ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ ❢♦r ♠❛❧ ❡s♣❡❝✐✜❝❛❞❛ ♥♦ ♠♦❞❡❧♦✳ ■st♦ é ♣♦ssí✈❡❧ s✐♠♣❧❡s♠❡♥t❡ ✐♥✈❡rt❡♥❞♦ ❛ ✈❛r✐á✈❡❧ q✉❡ ❡stá ❝♦♥❞✐❝✐♦♥❛❞❛✱ ✐st♦ é✱ ❛ss✉♠✐♥❞♦ q✉❡ ❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ t❡♠ ❞✐str✐❜✉✐çã♦ ❞❡ ❇❡r♥♦✉❧❧✐ ❡ q✉❡ ❛ ✈❛r✐á✈❡❧ ❝♦♥tí♥✉❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛✱ t❡♠ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳ ❖ ♠♦❞❡❧♦ ♣r♦♣♦st♦ ❡♠ ❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞ ✭✶✾✾✺✮ ♣♦❞❡ s❡r ✈✐st♦ ❝♦♠♦ ✉♠❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ❡♠ ❖❧❦✐♥ ✫ ❚❛t❡ ✭✶✾✻✶✮✳ ❯♠❛ ❡①t❡♥sã♦ ❞♦ ♠♦❞❡❧♦ ✐♥✐✲ ❝✐❛❧ ♣❛r❛ ♣❡r♠✐t✐r ❛❣r✉♣❛♠❡♥t♦ ❡♥tr❡ ❛s ♦❜s❡r✈❛çõ❡s t❛♠❜é♠ é ❛♣r❡s❡♥t❛❞❛ ✉t✐❧✐③❛♥❞♦ ❝♦♠♦ ❢❡rr❛♠❡♥t❛ ♦ ♠ét♦❞♦ ❞❡ ❡q✉❛çõ❡s ❞❡ ❡st✐♠❛çã♦ ❣❡♥❡r❛❧✐③❛❞❛s✳

✼

♦s ❝❛s♦s é ❛ss✉♠✐❞♦ q✉❡ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❞❛❞❛ ❛ ❞✐s❝r❡t❛✱ s❡❣✉❡ ❞✐str✐❜✉✐çã♦ ♥♦r♠❛❧✳ ◆♦ ♠♦❞❡❧♦ ❞❡ ❨❛♥❣ ❡t ❛❧✳ ✭✷✵✵✼✮✱ ❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ é ❛ss✉♠✐❞❛ s❡❣✉✐♥❞♦ ❞✐str✐❜✉✐çã♦ ❞❡ P♦✐ss♦♥ s❡♥❞♦ q✉❡ ♦ ♠♦❞❡❧♦ ✐♥✐❝✐❛❧ é t❛♠❜é♠ ❡st❡♥❞✐❞♦ ♣❛r❛ ❞❛❞♦s ❧♦♥❣✐t✉❞✐♥❛✐s✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♣♦ssí✈❡✐s ♠✉❞❛♥ç❛s ♥❛ ✈❛r✐â♥❝✐❛ ❡ ♥❛ ❝♦rr❡❧❛çã♦ ❞❡♥tr♦ ❞❡ ✉♠❛ ✉♥✐❞❛❞❡ s♦❜r❡ ♦ t❡♠♣♦ é ❝♦♥s✐❞❡r❛❞❛ ❡ s♦❧✉çõ❡s sã♦ ❛♣r❡s❡♥t❛❞❛s✳ ◆♦ ♠♦❞❡❧♦ ❞❡ ●❡♦r❣❡ ❡t ❛❧✳ ✭✷✵✵✼✮✱ ❛s s✉♣♦s✐çõ❡s ❞❡ q✉❡ ♦s ❞❛❞♦s sã♦ ♣❡r♠✉tá✈❡✐s ❡ q✉❡ ❛ ✈❛r✐á✈❡❧ ❞✐s❝r❡t❛ é ❜✐♥ár✐❛✱ sã♦ ❛❞♦t❛❞❛s✳ ❈♦♠♦ ❡♠ ❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞ ✭✶✾✾✺✮✱ ♦s ❛✉t♦r❡s ❛♣r❡s❡♥t❛♠ ♦ ♠♦❞❡❧♦ ✐♥✐❝✐❛❧♠❡♥t❡ ♣❛r❛ ❞❛❞♦s s❡♠ ❛❣r✉♣❛♠❡♥t♦ ❡ ♣♦st❡r✐♦r♠❡♥t❡ ♦ ❡st❡♥❞❡♠ ♣❛r❛ ♣❡r♠✐t✐r ♦ ❛❣r✉♣❛♠❡♥t♦✳

❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞ ✭✶✾✾✼✮ ❡ ❨❛♥❣ ✫ ❑❛♥❣ ✭✷✵✶✵✮ ❝♦♥s✐❞❡r❛♠ ♦s ♠♦❞❡❧♦s ❜✐✈❛r✐❛✲ ❞♦s ❛♣r❡s❡♥t❛❞♦s ❡♠ ❋✐t③♠❛✉r✐❝❡ ✫ ▲❛✐r❞ ✭✶✾✾✺✮ ❡ ❨❛♥❣ ❡t ❛❧✳ ✭✷✵✵✼✮✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ tr❛t❛♥❞♦ t❛♠❜é♠ ♦ ♣r♦❜❧❡♠❛ ♥♦ ❝♦♥t❡①t♦ ❡♠ q✉❡ ❤á ✈❛❧♦r❡s ❢❛❧t❛♥t❡s✳ ◆♦✈❛♠❡♥t❡✱ ❛ té❝♥✐❝❛ ❞❛ ❢❛t♦r❛çã♦ é ✉t✐❧✐③❛❞❛✳ ❘❡❝❡♥t❡♠❡♥t❡✱ ❙❛♠❛♥✐ ✫ ●❛♥❥❛❧✐ ✭✷✵✶✹✮ ♣r♦♣õ❡♠ ✉♠ ♠♦❞❡❧♦ ❞❡ r❡❣r❡ssã♦ ❜✐✈❛r✐❛❞♦ ❝♦♠ r❡s♣♦st❛s ❝♦rr❡❧❛❝✐♦♥❛❞❛s ♦r❞✐♥ár✐❛ ❡ ❜✐♥♦♠✐❛❧ ♥❡✲ ❣❛t✐✈❛ ✉t✐❧✐③❛♥❞♦ ❛ té❝♥✐❝❛ ❞❛ ❢❛t♦r❛çã♦ ♥❛ ❝♦♥str✉çã♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❥✉♥t❛✳ ❊❢❡✐t♦s ❛❧❡❛tór✐♦s ❛ss♦❝✐❛❞♦s às r❡s♣♦st❛s sã♦ ✐♥s❡r✐❞♦s ♥❛ ❝♦♥str✉çã♦ ❞♦ ♠♦❞❡❧♦✱ ♥♦ ❝♦♥t❡①t♦ ❞❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❛♣r❡s❡♥t❛❞❛ ✭●✉❡♦r❣✉✐❡✈❛✱ ✷✵✵✶✮✱ ♣❛r❛ ❛❝♦♠♦❞❛r ❛ ❝♦rr❡❧❛çã♦ ❡♥tr❡ ❛s r❡s♣♦st❛s ❧♦♥❣✐t✉❞✐♥❛✐s ❞❡ ✉♠ ♠❡s♠♦ ✐♥❞✐✈í❞✉♦✳ ❖ ♠♦❞❡❧♦ t❛♠❜é♠ ❝♦♥s✐❞❡r❛ ♦ ♣r♦❜❧❡♠❛ ❞❡ ❞❛❞♦s ❢❛❧t❛♥t❡s✳

✽

◆❡st❛ ♥♦✈❛ ❝❧❛ss❡ é ❛ss✉♠✐❞♦ q✉❡ ✉♠❛ ❞❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ é ❞✐s❝r❡t❛ ❡ ♣❡rt❡♥❝❡♥t❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ✉♥✐♣❛r❛♠étr✐❝❛ ♦✉ ❜✐♣❛r❛♠étr✐❝❛ ❡♥q✉❛♥t♦ q✉❡ ❛ ♦✉tr❛ r❡s♣♦st❛ é ❝♦♥s✐❞❡r❛❞❛ ❝♦♥tí♥✉❛ ❡ s✉❛ ❞✐str✐❜✉✐çã♦✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❞✐s❝r❡t❛✱ ♣❡rt❡♥❝❡♥t❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ✉♥✐♣❛r❛♠étr✐❝❛ ♦✉ ❜✐♣❛r❛♠étr✐❝❛✳

❈♦✈❛r✐á✈❡✐s ❡stã♦ ❞✐s♣♦♥í✈❡✐s ❡ sã♦ r❡❧❛❝✐♦♥❛❞❛s às ♠é❞✐❛s ❞❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞✐s✲ ❝r❡t❛ ❡ ❝♦♥tí♥✉❛ ♣♦r ♠❡✐♦ ❞❡ ❢✉♥çõ❡s ❞❡ ❧✐❣❛çã♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ♥❛t✉r❡③❛ ❞♦s ❞❛❞♦s✳ ❊♥tr❡t❛♥t♦✱ ❞✐❢❡r❡♥t❡♠❡♥t❡ ❞♦ q✉❡ ♦❝♦rr❡ ♥♦s ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❣❡♥❡r❛❧✐③❛❞♦s✱ ♦ ❝♦♠♣♦✲ ♥❡♥t❡ s✐st❡♠át✐❝♦ r❡❧❛❝✐♦♥❛❞♦ à ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ♦ ❝♦♠♣♦♥❡♥t❡ s✐st❡♠át✐❝♦ r❡❧❛❝✐♦♥❛❞♦ à ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ sã♦ ❢♦r♠❛❞♦s ♣♦r t❡r♠♦s ♣❛r❛♠étr✐❝♦s✱ ❝♦♠✲ ♣♦st♦s ❞❡ ❢✉♥çõ❡s ❧✐♥❡❛r❡s ❡ ♥ã♦ ❧✐♥❡❛r❡s ❡ ♣♦r t❡r♠♦s ♥ã♦ ♣❛r❛♠étr✐❝♦s ♥♦ ❝♦♥t❡①t♦ ❞♦s ♠♦❞❡❧♦s ❛❞✐t✐✈♦s ❣❡♥❡r❛❧✐③❛❞♦s s❡♠✐♣❛r❛♠étr✐❝♦ ✭●❆▼✮ ✭❍❛st✐❡ ✫ ❚✐❜s❤✐r❛♥✐✱ ✶✾✾✵✮✳ ◆❡st❡ s❡♥t✐❞♦✱ ❛ ❝❧❛ss❡ ♣r♦♣♦st❛ é ♠❛✐s ✢❡①í✈❡❧✱ ✉♠❛ ✈❡③ q✉❡ ❡♥❣❧♦❜❛ ✉♠❛ ✈❛r✐❡❞❛❞❡ ❞❡ ♠♦❞❡❧♦s✳ ❆ ❞❡♣❡♥❞ê♥❝✐❛ ❡①✐st❡♥t❡ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✱ r❡❧❡✈❛♥t❡ à ♠♦❞❡❧❛❣❡♠✱ é ✐♥s❡r✐❞❛ ♥❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ♣♦r ♠❡✐♦ ❞❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❞✐✲ ❝✐♦♥❛❧✳ ❉❡✜♥✐♥❞♦ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛✱ ❝♦♥s✐❞❡r❛✲s❡ q✉❡ ✉♠❛ tr❛♥s❢♦r♠❛çã♦ ❞❛ ♠é❞✐❛ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à r❡s♣♦st❛ ❞✐s❝r❡t❛✱ é ✉♠❛ ❢✉♥çã♦ ❧✐♥❡❛r ♦✉ ♥ã♦ ❧✐♥❡❛r ❝♦♥❤❡❝✐❞❛ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛✱ ❞❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥✲ ❝✐❛ ❡ ❞❛s ❝♦✈❛r✐á✈❡✐s ❛tr❛✈és ❞❛s ♠é❞✐❛s ♠❛r❣✐♥❛✐s✱ ❢❛③❡♥❞♦ ❝♦♠ q✉❡ ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s r❡s♣♦st❛s s❡❥❛ ❡①♣r❡ss❛❞❛✳

✾

◆❛ s❡q✉ê♥❝✐❛✱ é ❛♣r❡s❡♥t❛❞❛ ✉♠❛ té❝♥✐❝❛ ❞❡ ❡st✐♠❛çã♦ ♥ã♦ ♣❛r❛♠étr✐❝❛ ❞❡♥♦♠✐♥❛❞❛ P✲s♣❧✐♥❡✱ ♠✉✐t♦ ✉t✐❧✐③❛❞❛ ♥❛ ❡st✐♠❛çã♦ ♥ã♦ ♣❛r❛♠étr✐❝❛ ✉♥✐✈❛r✐❛❞❛✳ ❊ss❛ té❝♥✐❝❛ é ❡♥✲ tã♦ ❛❞❛♣t❛❞❛ ❛♦s ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❞❛ ❝❧❛ss❡✱ ❝✉❥♦s ♣r❡❞✐t♦r❡s ❝♦♥tê♠ ❛♣❡♥❛s ❢✉♥çõ❡s s✉❛✈❡s ❞♦s ❞❛❞♦s✱ ❡♠ ✉♠ ❝♦♥t❡①t♦ ♥ã♦ ♣❛r❛♠étr✐❝♦✳ ❚♦❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❡st✐♠❛çã♦ é ❞❡s❝r✐t♦ ❡♠ ❞❡t❛❧❤❡s✳ ❈♦♠♦ ❝♦♥s❡q✉ê♥❝✐❛ ❞❛ té❝♥✐❝❛ ❛♣❧✐❝❛❞❛✱ ♣♦❞❡✲s❡ ❛❥✉st❛r ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❡♥✈♦❧✈❡♥❞♦ ♣r❡❞✐t♦r❡s ❝♦♠ t❡r♠♦s ❧✐♥❡❛r❡s✱ ♥ã♦ ❧✐♥❡❛r❡s ❡ ♥ã♦ ♣❛r❛♠étr✐❝♦s✳ ❯♠❛ ✈❡③ ❛♣r❡s❡♥t❛❞♦s ♠ét♦❞♦s ❞❡ ❡st✐♠❛çã♦ ♣❛r❛ ♦s ♠♦❞❡❧♦s ❞❛ ❝❧❛ss❡✱ q✉❛tr♦ ♠♦❞❡❧♦s ♣❡rt❡♥❝❡♥t❡s à ❝❧❛ss❡ ❜✐✈❛r✐❛❞❛ ♣r♦♣♦st❛ sã♦ ❡①❡♠♣❧✐✜❝❛❞♦s✱ s❡♥❞♦ q✉❡ ❞♦✐s ❞❡❧❡s ♥ã♦ sã♦ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✳ ❊♠ r❡❧❛çã♦ à ♣❛rt❡ ❞❡ ❞✐❛❣♥óst✐❝♦✱ ♣r♦♣õ❡♠✲s❡ três r❡sí❞✉♦s ♣❛r❛ ❛ ❝❧❛ss❡ ♣r♦♣♦st❛✿ ♣❛❞r♦♥✐③❛❞♦✱ q✉❛♥t✐❧ ❡ ❝♦♠♣♦♥❡♥t❡s ❞❛ ❞❡s✈✐â♥❝✐❛✳ ❆❧é♠ ❞✐ss♦✱ ❝♦♥s✐❞❡r❛♠✲s❡ ❛s ♠❡❞✐❞❛s ✐♥✢✉ê♥❝✐❛ ❧♦❝❛❧ ❡ t♦t❛❧✱ út❡✐s ♣❛r❛ ❞❡t❡❝çã♦ ❞❡ ♣♦ssí✈❡✐s ♣♦♥t♦s ✐♥✢✉❡♥t❡s ♥♦s ♠♦❞❡❧♦s ♣❛r❛♠étr✐❝♦s✳ ◆❛ s❡q✉ê♥❝✐❛✱ ✉♠ ❡st✉❞♦ ❝♦♠ ❞❛❞♦s s✐♠✉❧❛❞♦s é r❡❛❧✐③❛❞♦ ❝♦♥s✐❞❡r❛♥❞♦ ♦s ♠♦❞❡❧♦s ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧ ❡ P♦✐ss♦♥✲ ♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦✱ ❛♠❜♦s ♣❡rt❡♥❝❡♥t❡s à ❝❧❛ss❡✳ P♦r ✜♠✱ ✉♠❛ ❛♣❧✐❝❛çã♦ ❛ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❞❛❞♦s r❡❛✐s ❝♦♥t❡♥❞♦ ✐♥❢♦r♠❛çõ❡s s♦❜r❡ ❛ ✐♥t❡r♥❛çã♦ ❞❡ ♣❛❝✐❡♥t❡s ❡♠ ✉♠ ❤♦s♣✐t❛❧ é ♣r♦♣♦st❛✱ ❝♦♥s✐❞❡r❛❞♦ ♦ ♠♦❞❡❧♦ ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧✳ ❆ ♦r❣❛♥✐③❛çã♦ ❞❛ t❡s❡ é ❞❡s❝r✐t❛ ❛❜❛✐①♦✳

✶✳✷ ❆♣r❡s❡♥t❛çã♦ ❞♦s ❝❛♣ít✉❧♦s

✶✵

◆♦ ❈❛♣ít✉❧♦ ✷ ✉♠❛ ❝❧❛ss❡ ❣❡r❛❧ ❞❡ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ♠✐st❛s é ✐♥tr♦❞✉③✐❞❛✱ ❡♠ q✉❡ s❡ ❝♦♥s✐❞❡r❛ q✉❡ ♦s ❝♦♠♣♦♥❡♥t❡s s✐st❡♠át✐❝♦s ❞❛s ♠é❞✐❛s ♠❛r❣✐♥❛✐s ❞❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛s sã♦ ❝♦♠♣♦st♦s ♣♦r t❡r♠♦s ❧✐♥❡❛r❡s ❡ ♥ã♦ ❧✐♥❡❛r❡s ♣❛r❛✲ ♠étr✐❝♦s ❝♦♥❤❡❝✐❞♦s ❡ t❛♠❜é♠ ♣♦r ❢✉♥çõ❡s ♥ã♦ ♣❛r❛♠étr✐❝❛s ❞❡ ❝♦✈❛r✐á✈❡✐s ❞✐s♣♦♥í✈❡✐s✳ ❆ ❝❧❛ss❡ ♣❛rt✐❝✉❧❛r✱ ❝♦♥s✐❞❡r❛♥❞♦ ❛♣❡♥❛s ♦s t❡r♠♦s ♣❛r❛♠étr✐❝♦s ♥♦s ♣r❡❞✐t♦r❡s✱ é ❡①✲ ♣❧♦r❛❞❛ ✐♥✐❝✐❛❧♠❡♥t❡ ❡♠ q✉❡ ✉♠ ♠ét♦❞♦ ❞❡ ❡st✐♠❛çã♦ ❝❧áss✐❝♦ é ❛♣r❡s❡♥t❛❞♦✳ ❉❡♣♦✐s✱ é ❛♣r❡s❡♥t❛❞❛ ❛ ♦✉tr❛ ❝❧❛ss❡ ♣❛rt✐❝✉❧❛r ❞❡ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❡♠ q✉❡ ♦s ✐♥t❡r❝❡♣t♦s sã♦ ❢♦r♠❛❞♦s ♣♦r t❡r♠♦s ❧✐♥❡❛r❡s ❡ ♥ã♦ ♣❛r❛♠étr✐❝♦s✳ ❯♠ ♠ét♦❞♦ ♣❛❞rã♦ ❞❡ ❡st✐♠❛çã♦ ✉♥✐✈❛r✐❛❞♦ é ❛♣r❡s❡♥t❛❞♦ ❡♠ q✉❡ sã♦ ❞❡st❛❝❛❞♦s ❛❧❣✉♥s ♣r♦❜❧❡♠❛s ❡♥❝♦♥tr❛❞♦s✳

◆♦ ❈❛♣ít✉❧♦ ✸ é ❛♣r❡s❡♥t❛❞❛ ❛ té❝♥✐❝❛ ❞❡ s✉❛✈✐③❛çã♦ P✲s♣❧✐♥❡✳ ❆s ♣r✐♥❝✐♣❛✐s ❝❛r❛❝✲ t❡ríst✐❝❛s ❞❛ té❝♥✐❝❛ sã♦ ✐❧✉str❛❞❛s ❛ss✐♠ ❝♦♠♦ s✉❛ ❛♣❧✐❝❛çã♦ ❛♦ ❝❛s♦ ✉♥✐✈❛r✐❛❞♦ ❝♦♠ ♣r❡❞✐t♦r ❢♦r♠❛❞♦ ♣♦r ✉♠❛ ♦✉ ♠❛✐s ❢✉♥çõ❡s s✉❛✈❡s ❞♦s ❞❛❞♦s✳ ❯♠❛ ❡①t❡♥sã♦ ❞❛ té❝♥✐❝❛ P✲s♣❧✐♥❡ ♣❛r❛ ❡st✐♠❛r ❛s ❢✉♥çõ❡s s✉❛✈❡s ♥♦s ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s é ❡♥tã♦ ♣r♦♣♦st❛✳ ❚♦❞♦ ♦ ♣r♦❝❡ss♦ ❞❡ ❡st✐♠❛çã♦ ❡ ✐♥❢❡rê♥❝✐❛ é ❛♣r❡s❡♥t❛❞♦✳

◆♦ ❈❛♣ít✉❧♦ ✹ q✉❛tr♦ ♠♦❞❡❧♦s ♣❡rt❡♥❝❡♥t❡s à ❝❧❛ss❡ ♣r♦♣♦st❛ sã♦ ✐❧✉str❛❞♦s ❡ s❡✉s r❡s♣❡❝t✐✈♦s ✈❡t♦r❡s ❡s❝♦r❡ ❡ ♠❛tr✐③❡s ❞❡ ✐♥❢♦r♠❛çã♦ ❡s♣❡r❛❞❛ ♦✉ ♦❜s❡r✈❛❞❛ sã♦ ♠♦str❛✲ ❞♦s✳ ❖s ♠♦❞❡❧♦s tr❛t❛❞♦s sã♦ ❇❡r♥♦✉❧❧✐✲♥♦r♠❛❧✱ P♦✐ss♦♥✲♥♦r♠❛❧✱ ❇❡r♥♦✉❧❧✐✲❡①♣♦♥❡♥❝✐❛❧ ❡ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦✳

◆♦ ❈❛♣ít✉❧♦ ✺ té❝♥✐❝❛s ❞❡ ❞✐❛❣♥óst✐❝♦ ❡ ✐♥✢✉ê♥❝✐❛ sã♦ ♣r♦♣♦st❛s ❡ ❛❞❛♣t❛❞❛s ♣❛r❛ ❛ ❝❧❛ss❡ ❣❡r❛❧ ❞❡ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✳

◆♦ ❈❛♣ít✉❧♦ ✻ ✉♠ ❡st✉❞♦ ❝♦♠ ❞❛❞♦s s✐♠✉❧❛❞♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ ♦ ♠♦❞❡❧♦ ❇❡r♥♦✉❧❧✐✲ ❡①♣♦♥❡♥❝✐❛❧ ❡ ♦ ♠♦❞❡❧♦ P♦✐ss♦♥✲♥♦r♠❛❧ s❡♠✐♣❛r❛♠étr✐❝♦ é ❛♣r❡s❡♥t❛❞♦✱ ❡♠ q✉❡ sã♦ ✈❡r✐✜❝❛❞♦s ❛s ♣r♦♣r✐❡❞❛❞❡s ❞♦s ❡st✐♠❛❞♦r❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❡ ❛s ♣❡r❢♦r✲ ♠❛♥❝❡s ❞♦s ❛❥✉st❡s ❡ r❡sí❞✉♦s✳

✶✶

●rá✜❝♦s ❞♦s r❡sí❞✉♦s ❡ ❞✐❛❣♥óst✐❝♦s sã♦ ♠♦str❛❞♦s✳

◆♦ ❈❛♣ít✉❧♦ ✽ ✉♠❛ ❝♦♥❝❧✉sã♦ ❞❡st❛ t❡s❡ é ❢❡✐t❛✱ ❡♥q✉❛♥t♦ q✉❡ ♥♦ ❈❛♣ít✉❧♦ ✾ tó♣✐❝♦s ♣❛r❛ ❛ s❡q✉ê♥❝✐❛ ❞♦ tr❛❜❛❧❤♦✱ ❝♦♠ ♣r♦♣♦st❛s ❞❡ ❝♦♥t✐♥✉✐❞❛❞❡✱ sã♦ ❧✐st❛❞❛s✳

❈❛♣ít✉❧♦ ✷

▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ♠✐st♦s

▼♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ♠✐st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✱ ❡♠ q✉❡ ❛ ❞✐str✐❜✉✐✲ çã♦ ❝♦♥❥✉♥t❛ ❞♦ ✈❡t♦r ❞❡ ✈❛r✐á✈❡✐s r❡s♣♦st❛ é ❞❛❞❛ ♣❡❧♦ ♣r♦❞✉t♦ ❡♥tr❡ ❛ ❞✐str✐❜✉✐çã♦ ♠❛r❣✐♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ❞✐s❝r❡t❛✱ tê♠ s✐❞♦ ✉t✐❧✐③❛❞♦s ❡♠ ❛❧❣✉♥s tr❛❜❛❧❤♦s ✭❋✐t③♠❛✉✲ r✐❝❡ ✫ ▲❛✐r❞✱ ✶✾✾✺❀ ❨❛♥❣ ❡t ❛❧✳✱ ✷✵✵✼✮✳ ❊♥tr❡t❛♥t♦✱ ♣♦✉❝♦s ♠♦❞❡❧♦s ♥❡st❛ ❧✐♥❤❛ sã♦ ❡♥❝♦♥tr❛❞♦s ♥❛ ❧✐t❡r❛t✉r❛✱ ❛ss✐♠ ❝♦♠♦ ❛ ❛✉sê♥❝✐❛ ❞❡ ✉♠ ♠♦❞❡❧♦ ❜✐✈❛r✐❛❞♦ ❝♦♠ r❡s♣♦s✲ t❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ ♠❛✐s ❣❡r❛❧✱ ❡♥❣❧♦❜❛♥❞♦ ♦✉tr♦s ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❥á ❡①✐st❡♥t❡s ♥❛ ❧✐t❡r❛t✉r❛✳

❖ ✐♥t❡r❡ss❡ ❡♠ ✉♠❛ ❝❧❛ss❡ ♠❛✐s ❣❡r❛❧ ❞❡ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ♠✐st❛s s❡ ❞❡✈❡ à ❣r❛♥❞❡ ✈❛r✐❡❞❛❞❡ ❞❡ ❝♦♥❥✉♥t♦s ❞❡ ❞❛❞♦s ❞✐s♣♦♥í✈❡✐s✱ t❡♥❞♦ ❛ss✐♠✱ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠♦❞❡❧♦s ♠❛✐s ✢❡①í✈❡✐s ❡ ❛❧t❡r♥❛t✐✈♦s✳ ❉❡st❛ ❢♦r♠❛✱ ✉♠❛ ❛♠♣❧❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ❞❡ r❡❣r❡ssã♦ ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ♠✐st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ é ❞❡✜♥✐❞❛ ♥❡st❡ ❝❛♣ít✉❧♦✳ P❛r❛ ✐st♦✱ é ❝♦♥s✐❞❡r❛❞♦ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ ❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ❞✐s❝r❡t❛✱ ♣❡rt❡♥❝❡♠ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧✳ ❆❧é♠ ❞✐ss♦✱ ❝♦✈❛r✐á✈❡✐s ❡stã♦ ❞✐s♣♦♥í✈❡✐s ❡ sã♦ r❡❧❛❝✐♦♥❛❞❛s às ♠é❞✐❛s ♠❛r❣✐♥❛✐s ♣♦r ♠❡✐♦ ❞❡ ❢✉♥çõ❡s ❞❡ ❧✐❣❛çã♦✱ ❡♠ q✉❡ ♦s ❝♦♠♣♦♥❡♥t❡s s✐st❡♠át✐❝♦s sã♦ ❝♦♠♣♦st♦s ♣♦r

✶✸

t❡r♠♦s ❧✐♥❡❛r❡s✱ ♥ã♦ ❧✐♥❡❛r❡s ❡ ♥ã♦ ♣❛r❛♠étr✐❝♦s✳ ❏á ❛ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s r❡s♣♦st❛s é ✐♥s❡r✐❞❛ ♥❛ ❝❧❛ss❡ ❞❡ ♠♦❞❡❧♦s ♣♦r ♠❡✐♦ ❞❛ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛✱ ❝♦♥❞✐❝✐♦♥❛❞❛ à ❞✐s❝r❡t❛✳

❙❡❥❛♠ Y1, Y2, . . . , Yn n ✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ❞✐s❝r❡t❛s ❡ ✐♥❞❡♣❡♥❞❡♥t❡s t❛✐s q✉❡ ❛ ❢✉♥✲ çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ Yi✱ i = 1, . . . , n✱ ♣❡rt❡♥❝❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ♥❛ ❢♦r♠❛ ❝❛♥ô♥✐❝❛✳ ❆ss✐♠✱

fYi(yi |θi, φ) = ❡①♣

yiθi−b(θi)

a(φ) +c(yi, φ)

, ✭✷✳✶✮

❡♠ q✉❡θi é ♦ ♣❛râ♠❡tr♦ ♥❛t✉r❛❧ ❡b(·)❡c(·)sã♦ ❢✉♥çõ❡s r❡❛✐s ❡s♣❡❝í✜❝❛s✳ ❆ ❢✉♥çã♦a(·) ❣❡r❛❧♠❡♥t❡ é ❞❛ ❢♦r♠❛ a(φ) = φ✱ s❡♥❞♦ φ ❞✐t♦ ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ ♦✉ ♣❛râ♠❡tr♦ ❞❡

❞✐s♣❡rsã♦✳ P❛r❛ ❛❧❣✉♠❛s ❞✐str✐❜✉✐çõ❡s ❞✐s❝r❡t❛s t❛✐s ❝♦♠♦ ❛s ❞✐str✐❜✉✐çõ❡s ❞❡ P♦✐ss♦♥ ❡ ❜✐♥♦♠✐❛❧✱φ é ❝♦♥❤❡❝✐❞♦✳ ❆ss✐♠✱ ❛ ❞✐str✐❜✉✐çã♦ é ❞✐t❛ ♣❡rt❡♥❝❡r à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧

✉♥✐♣❛r❛♠étr✐❝❛✳ P♦r ♦✉tr♦ ❧❛❞♦✱φ ♣♦❞❡ s❡r ❞❡s❝♦♥❤❡❝✐❞♦✳ ◆❡st❡s ❝❛s♦s✱ ❛ ❢❛♠í❧✐❛ ♥ã♦

♥❡❝❡ss❛r✐❛♠❡♥t❡ s❡rá ❡①♣♦♥❡♥❝✐❛❧ ❜✐♣❛r❛♠étr✐❝❛✳ P♦r s✐♠♣❧✐❝✐❞❛❞❡✱ s❡rá ❛ss✉♠✐❞♦ q✉❡ ❛ ❞✐str✐❜✉✐çã♦ ❞❡Yi ♣❡rt❡♥❝❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ✉♥✐♣❛r❛♠étr✐❝❛ ♦✉ ❜✐♣❛r❛♠étr✐❝❛✳

❉❡♥♦t❛♥❞♦ ♣♦r µiY ❛ ♠é❞✐❛ ♠❛r❣✐♥❛❧ ❞❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ ❞✐s❝r❡t❛ Yi✱ ✐st♦ é✱

µ_iY = E(Yi)✱ ❝♦♥s✐❞❡r❡ q✉❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝♦✈❛r✐á✈❡✐s zi1, zi2, . . . , zip✱ ❡st❡❥❛ ❞✐s♣♦✲ ♥í✈❡❧ ♣❛r❛ ♣r❡❞✐③❡r Yi✱ ♣❛r❛ ❝❛❞❛ ✉♥✐❞❛❞❡ i✱ i = 1, . . . , n✳ ◆♦ ❝♦♥t❡①t♦ ❞♦s ♠♦❞❡❧♦s ❛❞✐t✐✈♦s ❣❡♥❡r❛❧✐③❛❞♦s s❡♠✐♣❛r❛♠étr✐❝♦s✱ ❝♦♥s✐❞❡r❛♥❞♦ t❛♠❜é♠ ✉♠ t❡r♠♦ ♥ã♦ ❧✐♥❡❛r ♥♦ ♣r❡❞✐t♦r✱ r❡❧❛❝✐♦♥❛✲s❡ µ_iY às ❝♦✈❛r✐á✈❡✐s zi1, zi2, . . . , zip ♣♦r g1(µiY) = ηiY ❡♠ q✉❡

g1(·) é ✉♠❛ ❢✉♥çã♦ ♠♦♥ót♦♥❛ ❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❞❡♥♦t❛❞❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ❡ ηiY é ♦ ❝♦♠♣♦♥❡♥t❡ s✐st❡♠át✐❝♦✱ ❞❛❞♦ ♣♦r

ηiY = β0+β1zi1+· · ·+βkzik+h1(zik+1, . . . , zim, βk+1, . . . , βm) +h2(zim+1, . . . , zip)

✶✹

❛♠❡♥t❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❝♦♠ r❡s♣❡✐t♦ ❛♦s ❡❧❡♠❡♥t♦s ❞❡ B2✱ h2(·) é ✉♠❛ s♦♠❛ ❞❡ ❢✉♥çõ❡s ✉♥✐✈❛r✐❛❞❛s ❞❡s❝♦♥❤❡❝✐❞❛s✱ ✐st♦ é✱ h2(zim+1, . . . , zip) = Pp_jY=m+1sjY(zijY) s❡♥❞♦ sjY(·)

❢✉♥çõ❡s s✉❛✈❡s ♥ã♦ ❡s♣❡❝✐✜❝❛❞❛s ❞❡ ✉♠❛ ❢♦r♠❛ ♣❛r❛♠étr✐❝❛✱jY =m+ 1, m+ 2, . . . , p✱ ❡ ❛ss✐♠ s❡♥❞♦✱ ❡st✐♠❛❞❛s ♥♦ ❝♦♥t❡①t♦ ♥ã♦ ♣❛r❛♠étr✐❝♦ ❡ Zi1 = (1, zi1, . . . , zik)✱ Zi2 =

(zik+1, . . . , zim) ❡ Zi3 = (zim+1, . . . , zip) sã♦ ✈❡t♦r❡s ❝♦♠ ♦s ✈❛❧♦r❡s ❞❛s ❝♦✈❛r✐á✈❡✐s ❞✐s✲ ♣♦♥í✈❡✐s ♣❛r❛ ♣r❡❞✐③❡r Yi✱ i = 1,2, . . . , n✳ ▲♦❣♦✱ ♦ ❝♦♠♣♦♥❡♥t❡ s✐st❡♠át✐❝♦ ❞♦ ♠♦❞❡❧♦ é ♠❛✐s ❣❡r❛❧ ♥♦ s❡♥t✐❞♦ ❡♠ q✉❡ é ✉♠❛ s♦♠❛ ❞❡ t❡r♠♦s ❧✐♥❡❛r❡s✱ ❞❡ t❡r♠♦s ♥ã♦ ❧✐♥❡❛r❡s ♣❛r❛♠étr✐❝♦s ❡ ❞❡ t❡r♠♦s ♥ã♦ ♣❛r❛♠étr✐❝♦s ✭❍❛st✐❡ ✫ ❚✐❜s❤✐r❛♥✐✱ ✶✾✾✵✮✳

❆ ♠é❞✐❛ µiY é r❡❧❛❝✐♦♥❛❞❛ ❛♦ ♣❛râ♠❡tr♦ ♥❛t✉r❛❧ θi ♣♦r

µiY =b′(θi) =

d[b(θi)]

dθi

.

❙❡ g1(·) ❢♦r ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ❝❛♥ô♥✐❝❛✱ s❡❣✉❡ q✉❡ ηiY = θi ❡ ♥❡st❡ ❝❛s♦✱ é ❢á❝✐❧ ❡①♣r❡ss❛r(2.1)❡♠ ❢✉♥çã♦ ❞❡ µiY ♦✉ ❞❡ ηiY✳ ❆ ❢✉♥çã♦

b′′(θi) =

d2_[b(θ i)]

dθ2 i

é ❛ ❢✉♥çã♦ ❞❡ ✈❛r✐â♥❝✐❛ ❡ ♣♦❞❡ s❡r ❡①♣r❡ss❛ ❡♠ t❡r♠♦s ❞❡ µ_iY ♣♦r V(µ_iY)✱ ❡♠ q✉❡ V ar(Yi) = a(φ)V(µiY)✱ i= 1,2, . . . , n✳

❆♥❛❧♦❣❛♠❡♥t❡✱ s❡❥❛♠X1, X2, . . . , Xnn✈❛r✐á✈❡✐s ❛❧❡❛tór✐❛s ❝♦♥tí♥✉❛s ❡ ✐♥❞❡♣❡♥❞❡♥✲ t❡s t❛✐s q✉❡ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❝♦♥❞✐❝✐♦♥❛❧ ❞❡Xi✱ ❞❛❞♦ Yi =yi✱ i= 1, . . . , n✱ ♣❡rt❡♥❝❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ♥❛ ❢♦r♠❛ ❝❛♥ô♥✐❝❛✳ ❙❡❣✉❡ q✉❡

fXi|Yi(xi |yi, ϑi, ϕ) = ❡①♣

xiϑi−b∗(ϑi)

a∗_(ϕ) +c ∗_(x

i, ϕ)

, ✭✷✳✸✮

❡♠ q✉❡ b∗(_·) ❡ c∗(_·) sã♦ ❢✉♥çõ❡s r❡❛✐s ❡s♣❡❝í✜❝❛s✱ ϑi = ϑi(yi) é ♦ ♣❛râ♠❡tr♦ ♥❛t✉r❛❧ ♦ q✉❛❧ ❞❡♣❡♥❞❡ ❞♦ ✈❛❧♦r ♦❜s❡r✈❛❞♦ yi✱ i = 1, . . . , n ❡ a∗(·) é ✉♠❛ ❢✉♥çã♦ ❞❛ ❢♦r♠❛

a∗_{(ϕ) = ϕ✱ ❝♦♠ ϕ s❡♥❞♦ ♦ ♣❛râ♠❡tr♦ ❞❡ ❡s❝❛❧❛ ❝♦♥❤❡❝✐❞♦ ♦✉ ❞❡s❝♦♥❤❡❝✐❞♦✳ ❙❡ ϕ é} ❝♦♥❤❡❝✐❞♦✱ ❛ ❞✐str✐❜✉✐çã♦ é ❞✐t❛ ♣❡rt❡♥❝❡r ❛ ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ✉♥✐♣❛r❛♠étr✐❝❛✳ P❛r❛

✶✺

❡♠ (2.1)✱ s❡rá ❝♦♥s✐❞❡r❛❞♦ q✉❡ ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ Xi | Yi =yi ♣❡rt❡♥❝❡ à ❢❛♠í❧✐❛ ❡①♣♦♥❡♥❝✐❛❧ ✉♥✐♣❛r❛♠étr✐❝❛ ♦✉ ❜✐♣❛r❛♠étr✐❝❛✳

❆ss✐♠ ❝♦♠♦ ♦❝♦rr❡ ❝♦♠ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛Yi✱ ❛ss✉♠❡✲s❡ q✉❡ ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ❝♦✈❛r✐á✈❡✐sti1, ti2, . . . , tiq ❡st❡❥❛ ❞✐s♣♦♥í✈❡❧ ♣❛r❛ ♣r❡❞✐③❡r ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛

Xi✱i= 1,2, . . . , n✳ ❉❡♥♦t❛♥❞♦ ♣♦r µiX =E(Xi)❛ ♠é❞✐❛ ♠❛r❣✐♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛Xi✱ r❡❧❛❝✐♦♥❛✲s❡µiX às ❝♦✈❛r✐á✈❡✐s ❞✐s♣♦♥í✈❡✐s ♣♦rg2(µiX) =ηiX✱ ❡♠ q✉❡g2(·) é ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ♠♦♥ót♦♥❛ ❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡ η_iX é ♦ ❝♦♠♣♦♥❡♥t❡ s✐st❡♠át✐❝♦✱

❞❛❞♦ ♥♦ ❝♦♥t❡①t♦ ❞♦s ♠♦❞❡❧♦s ❛❞✐t✐✈♦s ❣❡♥❡r❛❧✐③❛❞♦s s❡♠✐♣❛r❛♠étr✐❝♦s ❝♦♠ ✉♠ t❡r♠♦ ♥ã♦ ❧✐♥❡❛r ♣♦r

η_iX = δ0 +δ1ti1+· · ·+δdtid+h3(tid+1, . . . , tio, δd+1, . . . , δo) +h4(tio+1, . . . , tiq)

= Ti1∆1+h3(Ti2,∆2) +h4(Ti3), ✭✷✳✹✮ ❡♠ q✉❡ ∆_{1 = (δ0, δ1, . . . , δd)}⊤ ❡ ∆_{2 = (δd+1, . . . , δo)}⊤ sã♦ ✈❡t♦r❡s ❞❡ ❝♦❡✜❝✐❡♥t❡s ❞❡ r❡❣r❡ssã♦ ❞❡s❝♦♥❤❡❝✐❞♦s✱ h3(·) é ✉♠❛ ❢✉♥çã♦ ♥ã♦ ❧✐♥❡❛r ❝♦♥❤❡❝✐❞❛✱ ❞✉❛s ✈❡③❡s ❝♦♥t✐✲ ♥✉❛♠❡♥t❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❝♦♠ r❡s♣❡✐t♦ ❛♦s ❡❧❡♠❡♥t♦s ❞♦ ✈❡t♦r ∆2✱ _{h4(tio+1, . . . , tiq) =}

Pq

jX=o+1ujX(tijX) s❡♥❞♦ ujX(·) ❢✉♥çõ❡s s✉❛✈❡s ♥ã♦ ❡s♣❡❝✐✜❝❛❞❛s ❞❡ ✉♠❛ ❢♦r♠❛ ♣❛r❛✲

♠étr✐❝❛✱jX =o+ 1, o+ 2, . . . , q✱ ❡ ❛ss✐♠ s❡♥❞♦✱ ❡st✐♠❛❞❛s ♥♦ ❝♦♥t❡①t♦ ♥ã♦ ♣❛r❛♠étr✐❝♦ ❡ Ti1 = (1, ti1, . . . , tid)✱ Ti2 = (tid+1, . . . , tio) ❡ Ti3 = (tio+1, . . . , tiq) sã♦ ✈❡t♦r❡s ❝♦♠ ♦s ✈❛❧♦r❡s ❞❛s ❝♦✈❛r✐á✈❡✐s ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♣r❡❞✐③❡rXi✱i= 1,2, . . . , n✳

❊♠ ❛❧❣✉♥s tr❛❜❛❧❤♦s ✭❚❛t❡✱ ✶✾✺✹❀ ❖❧❦✐♥ ✫ ❚❛t❡✱ ✶✾✻✶✮✱ ♦ ♦❜❥❡t✐✈♦ é ❡♥❝♦♥tr❛r ✉♠❛ ♠❡❞✐❞❛ ❞❡ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❛s r❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✳ ❊♥tr❡t❛♥t♦✱ ❡ss❡ ♥ã♦ s❡rá ♦ ❢♦❝♦ ❞❡st❡ tr❛❜❛❧❤♦✳ ◆ós ❡st❛♠♦s ✐♥t❡r❡ss❛❞♦s ♥❛ ✐♥s❡rçã♦ ❞❡ ✉♠❛ ❡str✉t✉r❛ ❞❡ ❞❡♣❡♥❞ê♥❝✐❛ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛✱ ♥❡❝❡ssár✐❛✱ ✉♠❛ ✈❡③ q✉❡ ❛s ✈❛r✐á✈❡✐s ♣♦❞❡♠ s❡r ♦❜s❡r✈❛❞❛s ❞❡ ✉♠ ♠❡s♠♦ ✐♥❞✐✈í❞✉♦ ♦✉ ❞❡ ✉♠ ♠❡s♠♦ ❡❧❡♠❡♥t♦ ❞❛ ♣♦♣✉❧❛çã♦✳ ❊st❛ ❞❡♣❡♥❞ê♥❝✐❛ é ❞❡t❡r♠✐♥❛❞❛ ♥♦ ♠♦❞❡❧♦ ♣❡❧❛ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❞❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛ Xi ❞❛❞❛ ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛ Yi✱ ❞❡♥♦t❛❞❛ ♣♦r

✶✻

❆ss✉♠❡✲s❡ q✉❡αi é r❡❧❛❝✐♦♥❛❞❛ à ♠é❞✐❛ ♠❛r❣✐♥❛❧ ❞❡Xi✱ à ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❞✐s❝r❡t❛

Yi✱ à ♠é❞✐❛ ♠❛r❣✐♥❛❧ ❞❡ Yi ❡ ❛ ✉♠ ♣❛râ♠❡tr♦ γ ✐♥❝❧✉í❞♦ ♥♦ ♠♦❞❡❧♦✱ q✉❡ ♣♦❞❡ s❡r ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝♦rr❡❧❛çã♦ ♦✉ ♦✉tr❛ ♠❡❞✐❞❛ ❞❡ ❛ss♦❝✐❛çã♦ ❡♥tr❡ ❛s ✈❛r✐á✈❡✐s r❡s♣♦st❛Xi ❡ Yi✱ ❞❡♣❡♥❞❡♥❞♦ ❞❛ ♥❛t✉r❡③❛ ❞♦s ❞❛❞♦s✱ ♣♦r g3(αi) =ξi✱ ❡♠ q✉❡ g3(·) é ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ♠♦♥ót♦♥❛ ❡ ❞✐❢❡r❡♥❝✐á✈❡❧ ❡ξi é ♦ ❝♦♠♣♦♥❡♥t❡ s✐st❡♠át✐❝♦✱ ❞❛❞♦ ♣♦r

ξi =h5(yi, µiY, µiX, γ), ✭✷✳✺✮

❡♠ q✉❡ h5(·) é ✉♠❛ ❢✉♥çã♦ ❧✐♥❡❛r ♦✉ ♥ã♦ ❧✐♥❡❛r ❝♦♥❤❡❝✐❞❛✱ ❞❡ ❝❧❛ss❡ C2✱ ❞♦ ✈❛❧♦r ♦❜s❡r✈❛❞♦ ❞❛ ✈❛r✐á✈❡❧ ❛❧❡❛tór✐❛ yi✱ ❞❛s ♠é❞✐❛s ♠❛r❣✐♥❛✐s µiY ❡ µiX ❡ ❞♦ ♣❛râ♠❡tr♦ ❞❡s❝♦♥❤❡❝✐❞♦ γ✳ ❆s ❡s❝♦❧❤❛s ❞❛s ❢✉♥çõ❡s g3(·) ❡ h5(·) ❞❡✈❡♠ s❡r t❛✐s q✉❡ ❛ ✐❣✉❛❧❞❛❞❡

E(αi) = µiX s❡❥❛ ✈❡r✐✜❝❛❞❛✱ ❥á q✉❡ E[E(Xi | Yi = yi)] = E(Xi) ❡ ♣♦r ❝♦♥str✉çã♦✱

E(Xi) = µiX✱ ❡♠ q✉❡

αi =g3−1(h5(yi, µiY, µiX, γ)). ✭✷✳✻✮ ❆ ♠é❞✐❛ ❝♦♥❞✐❝✐♦♥❛❧αi é r❡❧❛❝✐♦♥❛❞❛ ❛♦ ♣❛râ♠❡tr♦ ♥❛t✉r❛❧ ϑi ♣♦r

αi =b∗′(ϑi) =

d[b∗_(ϑ i)]

dϑi

.

❙❡g3(·)❢♦r ✉♠❛ ❢✉♥çã♦ ❞❡ ❧✐❣❛çã♦ ❝❛♥ô♥✐❝❛✱ s❡❣✉❡ q✉❡ξi =ϑi ❡ ❛ss✐♠✱ é ❢á❝✐❧ ❡①♣r❡ss❛r

(2.3) ❡♠ ❢✉♥çã♦ ❞❡αi ♦✉ ❞❡ ξi✳ ❆ ❢✉♥çã♦

b∗′′(ϑi) =

d2_[b∗_(ϑ i)]

dϑ2 i

é ❛ ❢✉♥çã♦ ❞❡ ✈❛r✐â♥❝✐❛ ❡ ♣♦❞❡ s❡r ❡①♣r❡ss❛ ❡♠ t❡r♠♦s ❞❡αi ♣♦rQ(αi)✱ ❡♠ q✉❡V ar(Xi |

Yi =yi) = a∗(ϕ)Q(αi)✳

❯t✐❧✐③❛♥❞♦ ❛s ❢✉♥çõ❡s (2.1)❡ (2.3)✱ é ♣♦ssí✈❡❧ ❡①♣r❡ss❛r ❛ ❢✉♥çã♦ ❞❡♥s✐❞❛❞❡ ❞❡ ♣r♦✲

❜❛❜✐❧✐❞❛❞❡ ❝♦♥❥✉♥t❛ ❞❡(Xi, Yi)❝♦♠♦

f_(Xi,Yi)(xi, yi|θi, ϑi, φ, ϕ) = fYi(yi |θi, φ)fXi|Yi(xi |yi, ϑi, ϕ)

= ❡①♣

yiθi−b(θi)

a(φ) +c(yi, φ)

❡①♣

xiϑi−b∗(ϑi)

a∗_(ϕ) +c ∗_(x

i, ϕ)

= ❡①♣

yiθi−b(θi)

a(φ) +

xiϑi−b∗(ϑi)

a∗_(ϕ) +c(yi, φ) +c ∗_(x

i, ϕ)

✶✼

✷✳✶ ▼♦❞❡❧♦ ♣❛r❛♠étr✐❝♦

❯♠ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❛ ❝❧❛ss❡ ❣❡r❛❧ ❞❡ ♠♦❞❡❧♦s ❜✐✈❛r✐❛❞♦s ❝♦♠ r❡s♣♦st❛s ❞✐s❝r❡t❛ ❡ ❝♦♥tí♥✉❛ ❛♣r❡s❡♥t❛❞❛ ❛❝✐♠❛ ♦❝♦rr❡ q✉❛♥❞♦h2(·)≡h4(·)≡0♥❛s ❡q✉❛çõ❡s(2.2)❡(2.4)✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ✐st♦ é✱ q✉❛♥❞♦ ♦s ❝♦♠♣♦♥❡♥t❡s s✐st❡♠át✐❝♦s ηiY ❡ηiX sã♦ ❝♦♠♣♦st♦s ♣♦r t❡r♠♦s ❧✐♥❡❛r❡s✱ ❝♦♠♦ ♦❝♦rr❡ ♥♦s ♠♦❞❡❧♦s ❧✐♥❡❛r❡s ❣❡♥❡r❛❧✐③❛❞♦s ✭▼❝❈✉❧❧❛❣❤ ✫ ◆❡❧❞❡r✱ ✶✾✽✾✮ ❡ ♣♦r ❢✉♥çõ❡s ♥ã♦ ❧✐♥❡❛r❡s ❝♦♥❤❡❝✐❞❛s✳ ❖s ❝♦♠♣♦♥❡♥t❡s s✐st❡♠át✐❝♦s sã♦ ❡♥tã♦✱ ❢♦r♠❛❞♦s ❛♣❡♥❛s ♣♦r t❡r♠♦s ♣❛r❛♠étr✐❝♦s✳ ❈♦♥s✐❞❡r❛♥❞♦ q✉❡p ❝♦✈❛r✐á✈❡✐s

❡st❡❥❛♠ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♣r❡❞✐③❡rYi✱ i = 1,2, . . . , n✱ ♦ ♣r❡❞✐t♦r ηiY ❞❛❞♦ ♣❡❧❛ ❡q✉❛çã♦

(2.2) s❡ r❡❞✉③ ❛

η_iY = β0+β1zi1+· · ·+βkzik+h1(zik+1, . . . , zip, βk+1, . . . , βp)

= Zi1B1 +h1(Zi2,B2), ✭✷✳✽✮

❝♦♠B1 = (β0, β1, . . . , βk)⊤✱B2 = (βk+1, . . . , βp)⊤✱Zi1 = (1, zi1, . . . , zik)❡Zi2 = (zik+1✱

. . . , zip)✳ ❆♥❛❧♦❣❛♠❡♥t❡✱ s✉♣♦♥❞♦ q✉❡ q ❝♦✈❛r✐á✈❡✐s ❡st❡❥❛♠ ❞✐s♣♦♥í✈❡✐s ♣❛r❛ ♣r❡❞✐③❡r ❛ ✈❛r✐á✈❡❧ r❡s♣♦st❛ ❝♦♥tí♥✉❛Xi✱ i= 1,2, . . . , n✱ ♦ ♣r❡❞✐t♦r ηiX ❞❛❞♦ ♣❡❧❛ ❡q✉❛çã♦ (2.4) s❡ r❡❞✉③ ❛

ηiX = δ0+δ1ti1+· · ·+δdtid+h3(tid+1, . . . , tiq, δd+1, . . . , δq)

= Ti1∆1+h3(Ti2,∆2), ✭✷✳✾✮

❝♦♠ ∆_{1 = (δ0, δ1, . . . , δd)}⊤✱ ∆_{2 = (δd+1, . . . , δq)}⊤✱ _{Ti1 = (1, ti1, . . . , tid)} ❡ _{Ti2 = (tid}+1✱

. . . , tiq)✳ P❛r❛ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❛♣r❡s❡♥t❛❞♦ ♥❡st❛ s❡çã♦✱ ✉t✐❧✐③❛♠♦s ♦ ♠ét♦❞♦ ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛✳

✷✳✶✳✶ ▼á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛

❙❡❥❛♠ (x1, y1),(x2, y2), . . . ,(xn, yn) ✉♠ ❝♦♥❥✉♥t♦ ❞❡ ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s ❞❡(X1, Y1)✱

✶✽

✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❡ β= (B₁⊤,B₂⊤)⊤_{✱ ∆= (∆}⊤

1,∆⊤2)⊤✱ γ✱φ ❡ϕ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦

L(β,∆, γ, φ, ϕ_|x,y,Z,T) =

n

Y

i=1

Li(β,∆, γ, φ, ϕ|xi, yi,Zi1,Zi2,Ti1,Ti2)

=

n

Y

i=1

f_(Xi,Yi)(xi, yi |β,∆, γ, φ, ϕ,Zi1,Zi2,Ti1,Ti2)

= n Y i=1 ❡①♣

yiθi−b(θi)

a(φ) +

xiϑi−b∗(ϑi)

a∗_(ϕ) +c(yi, φ) +c ∗_(x

i, ϕ)

= ❡①♣

(

1

a(φ)

n

X

i=1

[yiθi−b(θi)] +

1

a∗_(ϕ) n

X

i=1

[xiϑi−b∗(ϑi)]

)

×❡①♣

( _n X

i=1

c(y_i, φ) +

n

X

i=1

c∗(x_i, ϕ)

)

, ✭✷✳✶✵✮

❡♠ q✉❡ x= (x1, x2, . . . , xn)⊤✱ y = (y1, y2, . . . , yn)⊤✱ Z1 = (Z11⊤,Z21⊤, . . . ,Zn⊤1)⊤✱ Z2 =

(Z₁₂⊤,Z₂₂⊤, . . . ,Z_n⊤₂)⊤_{✱Z = (Z}

1,Z2)✱T1 = (T11⊤,T21⊤, . . . ,Tn⊤1)⊤✱T2 = (T12⊤,T22⊤, . . . ,Tn⊤2)⊤ ❡T = (T1,T2)✳

❆ ❢✉♥çã♦ ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❡β = (B⊤₁,B₂⊤)⊤_{✱ ∆= (∆}⊤

1,∆⊤2)⊤✱ γ✱ φ ❡ϕ✱ ❞❛❞❛ ✉♠❛ ❛♠♦str❛ ❞❡ t❛♠❛♥❤♦ n✱ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦

ℓ(β,∆_{, γ, φ, ϕ|x,y,Z,T) =} n X

i=1

ℓi(β,∆, γ, φ, ϕ|xi, yi,Zi1,Zi2,Ti1,Ti2)

= 1

a(φ)

n X

i=1

[yiθi−b(θi)] +

1 a∗_(ϕ)

n X

i=1

[xiϑi−b∗(ϑi)]

+

n X

i=1

c(yi, φ) + n X

i=1

c∗(xi, ϕ). ✭✷✳✶✶✮

❆s ❡q✉❛çõ❡s ❞❡ ♠á①✐♠❛ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ sã♦ ❢❛❝✐❧♠❡♥t❡ ♦❜t✐❞❛s ❡ ❢♦r♠❛♠ ✉♠ ❝♦♥✲ ❥✉♥t♦ ❞❡p+q+ 5❡q✉❛çõ❡s ❝♦rr❡s♣♦♥❞❡♥t❡s ❛♦s ♣❛râ♠❡tr♦sβ0, β1, . . . , βp, δ0, δ1, . . . , δq,

γ, φ ❡ ϕ✳ ❙❡❥❛ U = (U(β)⊤_,U(∆)⊤_{, U(γ),U(φ)✱ U(ϕ))}⊤ _{♦ ✈❡t♦r ❡s❝♦r❡ ❞❛ ❢✉♥çã♦} ❧♦❣✲✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞❛❞❛ ♥❛ ❡q✉❛çã♦(2.11)✳ ❖s ❡❧❡♠❡♥t♦s ❞♦s ✈❡t♦r❡sU(β)❡U(∆₎❡ ♦s ❝♦♠♣♦♥❡♥t❡sU(γ)✱U(φ)❡U(ϕ)sã♦ ❞❛❞♦s ❡♠ ❞❡t❛❧❤❡s ♥♦ ❆♣ê♥❞✐❝❡ A✳ ❊♠ ❢♦r♠❛