Avaliação da proficiência em inglês acadêmico
através de um teste adaptativo informatizado
Avaliação da proficiência em inglês acadêmico através de
um teste adaptativo informatizado
Vanessa Rufino da Silva
Orientadora:
Profa. Dra. Mariana Cúri
Dissertação apresentada ao Instituto de Ciências Matemáticas e de Computação - ICMC-USP e ao Departamento de Estatística – DEs-UFSCar, como parte dos requisitos para obtenção do título de Mestre em Estatística – Interinstitucional de Pós-Graduação em Estatística. VERSÃO REVISADA
USP/UFSCar
–
São Carlos
Abril de 2015
SERVIÇO DE PÓS-GRADUAÇÃO DO ICMC-USP
Data de Depósito:
Ficha catalográfica elaborada pela Biblioteca Prof. Achille Bassi e Seção Técnica de Informática, ICMC/USP,
com os dados fornecidos pelo(a) autor(a)
R586a
Rufino da Silva, Vanessa
Avaliação da proficiência em inglês acadêmico através de um teste adaptativo informatizado / Vanessa Rufino da Silva; orientadora Mariana Cúri. -- São Carlos, 2015.
33 p.
Dissertação (Mestrado - Programa
Interinstitucional de Pós-graduação em Estatística) --Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, 2015.
❆❣r❛❞❡❝✐♠❡♥t♦s
Pr✐♠❡✐r❛♠❡♥t❡ ❛♦ ♠❡✉ ♣❛✐✱ ❆❧t❛✐r ❘✉✜♥♦ ❞❛ ❙✐❧✈❛ ♣❡❧♦ ❛♠♦r ❡ ❛♣♦✐♦ ♣❛r❛ q✉❡ ❡✉ ❝♦♥s❡❣✉✐ss❡ ❝♦♥❝❧✉✐r ❡ss❛ ❥♦r♥❛❞❛ ❞❡✐①❛♥❞♦ q✉❡ ❡✉ ♥✉♥❝❛ ♠❡ s❡♥t✐ss❡ s♦③✐♥❤❛✳
❆♦ ♠❡✉ ✐r♠ã♦✱ ❋❡❧✐♣❡ ❘✉✜♥♦ ❞❛ ❙✐❧✈❛ ♣❡❧♦s ✜♥s ❞❡ s❡♠❛♥❛ ❥♦❣❛♥❞♦ ✈✐❞❡♦ ❣❛♠❡ ❡ ♣❡❧♦ s❡✉ s♦rr✐s♦ ❡ ❛❧❡❣r✐❛ ♣❛r❛ q✉❡ ♣✉❞❡ss❡ r❡❧❛①❛r ❡ ❞❛r ♠❛✐s ♠♦t✐✈❛çã♦ ♣❛r❛ ❝♦♥t✐♥✉❛r✳
➚ ♠✐♥❤❛ ♠ã❡✱ ●✐s❧❡♥❡ ▼❛r✐❛ ❞❡ ▲✐♠❛ ❙✐❧✈❛ q✉❡ ♠❡s♠♦ ♥ã♦ ❡st❛♥❞♦ ♠❛✐s ✜s✐❝❛♠❡♥t❡ ♣r❡s❡♥t❡ t❡♥❤♦ ❝❡rt❡③❛ q✉❡ s❡♠♣r❡ ❡st❡✈❡ ❛♦ ♠❡✉ ❧❛❞♦ ♠❡ ❞❛♥❞♦ ❢♦rç❛✳
❆♦ ♠❡✉ ♥❛♠♦r❛❞♦✱ ●❡♦r❣❡ ▲✉❝❛s ▼♦r❛❡s P❡③③♦tt✱ ♠❡✉ ❣r❛♥❞❡ ✐♥❝❡♥t✐✈❛❞♦r✱ ♣♦r s❡♠♣r❡ ♠❡ ❛❥✉❞❛r q✉❛♥❞♦ ♥❡❝❡ssár✐♦✱ ♣❡❧❛ ❝♦♠♣r❡❡♥sã♦✱ ♣❡❧♦ ❛♠♦r✱ ❝❛r✐♥❤♦ ❡ ❝♦♠♣❛♥❤❡✐r✐s♠♦✳
➚ ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ ▼❛r✐❛♥❛ ❈úr✐✱ ♣❡❧❛ s❛❜❡❞♦r✐❛ ♥❛ ♦r✐❡♥t❛çã♦✱ ♣♦r ❝♦♠♣❛rt✐❧❤❛r s❡✉s ❝♦♥❤❡✲ ❝✐♠❡♥t♦s✱ ♣♦r s✉❛ ❝♦♠♣r❡❡♥sã♦ ❡ ❛✉①í❧✐♦ ♣❛r❛ ❛❧❝❛♥ç❛r♠♦s ♠❛✐s ❡ss❛ ✈✐tór✐❛✳
➚ ♠✐♥❤❛ ❛♠✐❣❛ ◆❛②❛r❛ P❡❣♦r❛r♦ ❘❡✐♥❛ ♣♦r s❡♠♣r❡ ♦✉✈✐r ♠✐♥❤❛s r❡❝❧❛♠❛çõ❡s✱ ♣❡❧❛s ❢ér✐❛s ♠❛r❛✈✐❧❤♦s❛s ❡ ♣♦r ♠❡ ❛♣♦✐❛r s❡♠♣r❡✳
➚ ❈❆P❊❙ ♣❡❧♦ ❛♣♦✐♦ ✜♥❛♥❝❡✐r♦✳
◆ã♦ ♣♦❞❡r✐❛ ❞❡✐①❛r ❞❡ ❛❣r❛❞❡❝❡r ❛♦s ♣r♦❢❡ss♦r❡s✱ ❢✉♥❝✐♦♥ár✐♦s✱ ❛♠✐❣♦s ❡ ❝♦❧❡❣❛s ❞❛ ❯❋❙❈❛r ❡ ❯❙P✳
❊♥✜♠✱ à t♦❞♦s q✉❡ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ♠❡ ❛❥✉❞❛r❛♠ ♥❛ ❝♦♥❝r❡t✐③❛çã♦ ❞❡st❡ s♦♥❤♦✳
❘❡s✉♠♦
❊st❡ tr❛❜❛❧❤♦ ❞❡s❝r❡✈❡ ❛s ❡t❛♣❛s ❞❡ tr❛♥s❢♦r♠❛çã♦ ❞❡ ✉♠ ❡①❛♠❡ ❞❡ ♣r♦✜❝✐ê♥❝✐❛ ❡♠ ✐♥❣❧ês ❛❝❛✲ ❞ê♠✐❝♦✱ ❛♣❧✐❝❛❞♦ ✈✐❛ ❧á♣✐s✲❡✲♣❛♣❡❧✱ ❝♦♠ ✐t❡♥s ❞❡ ♠ú❧t✐♣❧❛ ❡s❝♦❧❤❛ ❛❞♠✐♥✐str❛❞♦s s❡❣✉♥❞♦ ♦ ♠ét♦❞♦
❞❡ ▼❡❞✐❞❛ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❆❞♠✐ssí✈❡❧ ✭❙❤✉❢♦r❞ ❏r ❡t ❛❧✳✱ ✶✾✻✻✮✱ ✉t✐❧✐③❛❞♦ ♥♦ ♣r♦❣r❛♠❛ ❞❡ ♣ós✲
❣r❛❞✉❛çã♦ ❞♦ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦ ❞❛ ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦ ✭■❈▼❈✲❯❙P✮✱ ❡♠ ✉♠ t❡st❡ ❛❞❛♣t❛t✐✈♦ ✐♥❢♦r♠❛t✐③❛❞♦ ✭❚❆■✲P■✮ ❜❛s❡❛❞♦ ❡♠ ✉♠ ♠♦❞❡❧♦ ❞❛ ❚❡♦r✐❛ ❞❡ ❘❡s♣♦st❛ ❛♦ ■t❡♠ ✭❚❘■✮✳ ❆♣❡s❛r ❞♦ ♣r♦❣r❛♠❛ ❛❝❡✐t❛r ❞✐✈❡rs♦s ❡①❛♠❡s q✉❡ ❛t❡st❛♠ ❛ ♣r♦✜❝✐✲ ê♥❝✐❛ ❡♠ ✐♥❣❧ês ♣❛r❛ ✐♥❞✐✈í❞✉♦s ♥ã♦✲♥❛t✐✈♦s ❞❡ ❛❜r❛♥❣ê♥❝✐❛ ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ✐♥t❡r♥❛❝✐♦♥❛✐s✱ ❝♦♠♦ ♦ ❚❖❊❋▲ ✭❚❡st ♦❢ ❊♥❣❧✐s❤ ❛s ❛ ❋♦r❡✐❣♥ ▲❛♥❣✉❛❣❡✮✱ ■❊▲❚❙ ✭■♥t❡r♥❛t✐♦♥❛❧ ❊♥❣❧✐s❤ ▲❛♥❣✉❛❣❡ ❚❡s✲ t✐♥❣ ❙②st❡♠✮ ❡ ❈P❊ ✭❈❡rt✐✜❝❛t❡ ♦❢ Pr♦✜❝✐❡♥❝② ✐♥ ❊♥❣❧✐s❤✮✱ ♣♦r ❡①❡♠♣❧♦✱ ❛ s✉❛ ♦❜r✐❣❛t♦r✐❡❞❛❞❡ é ✐♥❝♦❡r❡♥t❡ ❡♠ ✉♥✐✈❡rs✐❞❛❞❡s ♣ú❜❧✐❝❛s ❞♦ ❇r❛s✐❧ ❞❡✈✐❞♦ ❛♦ ❝✉st♦ q✉❡ ✈❛r✐❛ ❞❡ ✷✵✵ ❛ ✸✵✵ ❞ó❧❛r❡s ♣♦r ❡①❛♠❡✳ ❖ s♦❢t✇❛r❡ ❚❆■✲P■ ✭❚❡st❡ ❆❞❛♣t❛t✐✈♦ ■♥❢♦r♠❛t✐③❛❞♦ ♣❛r❛ Pr♦✜❝✐ê♥❝✐❛ ❡♠ ■♥❣❧ês✮✱ q✉❡ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ❏❛✈❛ ❡ ❙◗▲✐t❡✱ s❡rá ✉t✐❧✐③❛❞♦ ♣❛r❛ ❛ ❛✈❛❧✐❛çã♦ ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❡♠ ✐♥❣❧ês ❞♦s ❛❧✉♥♦s ❞♦ ♣r♦❣r❛♠❛ ❛ ♣❛rt✐r ❞♦ s❡❣✉♥❞♦ s❡♠❡str❡ ❞❡ ✷✵✶✸✱ ❞❡ ❢♦r♠❛ ❣r❛t✉✐t❛✳ ❆ ♠❡t♦❞♦❧♦❣✐❛ ❡st❛tíst✐❝❛ ✐♠♣❧❡♠❡♥t❛❞❛ ❢♦✐ ❞❡✜♥✐❞❛ ❝♦♥s✐❞❡r❛♥❞♦ ❛ ❤✐stór✐❛ ❡ ♦❜❥❡t✐✈♦s ❞♦ ❡①❛♠❡ ❡ ❛❞♦t♦✉ ♦ ♠♦❞❡❧♦ ❞❡ r❡s✲
♣♦st❛ ❣r❛❞✉❛❧ ✉♥✐❞✐♠❡♥s✐♦♥❛❧ ❞❡ ❙❛♠❡❥✐♠❛ ✭❙❛♠❡❥✐♠❛✱ ✶✾✻✾✮✱ ♦ ❝r✐tér✐♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ♣❛r❛
s❡❧❡çã♦ ❞❡ ✐t❡♥s✱ ♦ ♠ét♦❞♦ ❞❡ ❡st✐♠❛çã♦ ❞❛ ❡s♣❡r❛♥ç❛ ❛ ♣♦st❡r✐♦r✐ ♣❛r❛ ♦s tr❛ç♦s ❧❛t❡♥t❡s ✭❇❛❦❡r
✱✷✵✵✶✮ ❡ ❛ ❛❜♦r❞❛❣❡♠ ❙❤❛❞♦✇ t❡st ✭❱❛♥ ❞❡r ▲✐♥❞❡♥ ✫ P❛s❤❧❡②✱✷✵✶✵✮ ♣❛r❛ ✐♠♣♦s✐çã♦ ❞❡ r❡str✐çõ❡s
✭❞❡ ❝♦♥t❡ú❞♦ ❡ t❛♠❛♥❤♦ ❞❛ ♣r♦✈❛✮ ♥❛ ❝♦♠♣♦s✐çã♦ ❞♦ t❡st❡ ❞❡ ❝❛❞❛ ✐♥❞✐✈í❞✉♦✳ ❯♠❛ ❞❡s❝r✐çã♦ ❞❛ ❡str✉t✉r❛ ❞♦ ❡①❛♠❡✱ ❞♦s ♠ét♦❞♦s ❡♠♣r❡❣❛❞♦s✱ ❞♦s r❡s✉❧t❛❞♦s ❞❛s ❛♣❧✐❝❛çõ❡s ❞♦ ❚❆■✲P■ ❛ ❛❧✉♥♦s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❞♦ ■❈▼❈ ❡ ❡st✉❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❞♦s ❛❧✉♥♦s ❡♠ ❛♣r♦✈❛❞♦s ❡ r❡♣r♦✈❛❞♦s✱ sã♦ ❛♣r❡✲ s❡♥t❛❞♦s ♥❡st❡ tr❛❜❛❧❤♦✱ ❡✈✐❞❡♥❝✐❛♥❞♦ ❛ ❜♦❛ q✉❛❧✐❞❛❞❡ ❞❛ ♥♦✈❛ ♣r♦♣♦st❛ ❛❞♦t❛❞❛ ❡ ❛♣r✐♠♦r❛♠❡♥t♦ ❞♦ ❡①❛♠❡ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞♦s ♠ét♦❞♦s ❞❡ ❚❘■ ❡ ❚❆■✳
P❛❧❛✈r❛s✲❝❤❛✈❡✿ t❡st❡ ❛❞❛♣t❛t✐✈♦ ❝♦♠♣✉t❛❞♦r✐③❛❞♦✱ t❡♦r✐❛ ❞❡ r❡s♣♦st❛ ❛♦ ✐t❡♠✱ s❤❛❞♦✇ t❡st✳
❆❜str❛❝t
❚❤✐s ✇♦r❦ ❞❡s❝r✐❜❡s t❤❡ st❡♣s ❢♦r ❝♦♥✈❡rt✐♥❣ ❛ ❧✐♥❡❛r ♣❛♣❡r✲❛♥❞✲♣❡♥❝✐❧ ❊♥❣❧✐s❤ ♣r♦✜❝✐❡♥❝② t❡st ❢♦r ❛❝❛❞❡♠✐❝ ♣✉r♣♦s❡s✱ ❝♦♠♣♦s❡❞ ✇✐t❤ ♠✉❧t✐♣❧❡ ❝❤♦✐❝❡ ✐t❡♠s t❤❛t ❛r❡ ❛❞♠✐♥✐st❡r❡❞ ❢♦❧❧♦✇✐♥❣ t❤❡
❛❞♠✐ss✐❜❧❡ ♣r♦❜❛❜✐❧✐t② ♠❡❛s✉r❡♠❡♥t ♣r♦❝❡❞✉r❡ ✭❙❤✉❢♦r❞ ❏r ❡t ❛❧✳✱ ✶✾✻✻✮✱ ❛❞♦♣t❡❞ ❜② t❤❡ ❣r❛❞✉❛t❡
♣r♦❣r❛♠ ♦❢ ■♥st✐t✉t❡ ♦❢ ▼❛t❤❡♠❛t✐❝❛❧ ❙❝✐❡♥❝❡s ❛♥❞ ❈♦♠♣✉t✐♥❣ ♦❢ ❯♥✐✈❡rs✐t② ♦❢ ❙ã♦ P❛✉❧♦ ✭■❈▼❈✲ ❯❙P✮✱ ❇r❛③✐❧✱ t♦ ❛ ❝♦♠♣✉t❡r✐③❡❞ ❛❞❛♣t✐✈❡ t❡st ✭❈❆❚✮ ❜❛s❡❞ ♦♥ ❛♥ ✐t❡♠ r❡s♣♦♥s❡ t❤❡♦r② ♠♦❞❡❧ ✭■❘❚✮✳ ❉❡s♣✐t❡ t❤❡ ■♥st✐t✉t❡ r❡❝♦❣♥✐③❡s r❡❧✐❛❜❧❡ ✐♥t❡r♥❛t✐♦♥❛❧ ❊♥❣❧✐s❤✲❧❛♥❣✉❛❣❡ ❡①❛♠s ❢♦r ❛❝❛❞❡♠✐❝ ♣✉r♣♦s❡s ❛♥❞ ♥♦♥✲♥❛t✐✈❡ s♣❡❛❦❡rs✱ ❛s ❚❖❊❋▲ ✭❚❡st ♦❢ ❊♥❣❧✐s❤ ❛s ❛ ❋♦r❡✐❣♥ ▲❛♥❣✉❛❣❡✮✱ ■❊▲❚❙ ✭■♥t❡r♥❛t✐♦♥❛❧ ❊♥❣❧✐s❤ ▲❛♥❣✉❛❣❡ ❚❡st✐♥❣ ❙②st❡♠✮ ❛♥❞ ❈P❊ ✭❈❛♠❜r✐❞❣❡ ❊♥❣❧✐s❤✿ Pr♦✜❝✐❡♥❝②✮✱ ❢♦r ✐♥st❛♥❝❡✱ ✐t ✐s ✐♥❝♦♥s✐st❡♥t t❤❛t ♣✉❜❧✐❝ ✉♥✐✈❡rs✐t✐❡s ✐♥ ❇r❛③✐❧ r❡q✉✐r❡ t❤❡♠ ❛s ❝❡rt✐✜❝❛t✐♦♥ ❜❡❝❛✉s❡ ♦❢ t❤❡ ❝♦st ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ❯❙✩ ✷✵✵✳✵✵ t♦ ❯❙✩ ✸✵✵✳✵✵ ♣❡r ❡①❛♠✳ ❚❤❡ s♦❢t✇❛r❡ ❚❆■✲P■ ✭❝♦♠♣✉t❡r✐③❡❞ ❛❞❛♣t✐✈❡ t❡st ❢♦r ❊♥❣❧✐s❤ ♣r♦✜❝✐❡♥❝②✮ ✇❛s ✐♠♣❧❡♠❡♥t❡❞ ✐♥ ❏❛✈❛ ❧❛♥❣✉❛❣❡✱ ✉s❡❞ ❙◗▲✐t❡ ❛s ❞❛t❛❜❛s❡ ❡♥❣✐♥❡✱ ❛♥❞ ✐t s❤❛❧❧ ❜❡ ♦✛❡r❡❞ ❢r❡❡ ♦❢ ❝❤❛r❣❡ ❢♦r ❊♥❣❧✐s❤ ♣r♦✜❝✐❡♥❝② ❛ss❡ss♠❡♥t ♦❢ t❤❡ ❣r❛❞✉❛t❡ st✉❞❡♥ts ❢r♦♠ ❖❝t♦❜❡r ✷✵✶✸✳ ❚❤❡ st❛t✐st✐❝❛❧ ♠❡t❤♦❞♦❧♦❣② ❡♠♣❧♦②❡❞ ❢♦r ❚❆■✲P■ ❝♦♥str✉❝t✐♦♥ ✇❛s ❞❡✜♥❡❞ ❝♦♥s✐❞❡r✐♥❣ t❤❡ ❤✐st♦r② ❛♥❞ t❤❡ ❛✐♠s ♦❢ t❤❡ ❡✈❛❧✉❛t✐♦♥ ❛♥❞ ❛❞♦♣t❡❞ t❤❡ ❙❛♠❡❥✐♠❛✬s ❣r❛❞❡❞
r❡s♣♦♥s❡ ♠♦❞❡❧ ✭❙❛♠❡❥✐♠❛✱✶✾✻✾✮✱ t❤❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ✐♥❢♦r♠❛t✐♦♥ ❝r✐t❡r✐♦♥ ❢♦r ✐t❡♠ s❡❧❡❝t✐♦♥✱ t❤❡
❡①♣❡❝t❡❞ ❛ ♣♦st❡r✐♦r✐ ❇❛②❡s✐❛♥ ❡st✐♠❛t✐♦♥ ❢♦r ❧❛t❡♥t tr❛✐t ✭❇❛❦❡r✱✷✵✵✶✮ ❛♥❞ s❤❛❞♦✇ t❡st ❛♣♣r♦❛❝❤
✭❱❛♥ ❞❡r ▲✐♥❞❡♥ ✫ P❛s❤❧❡②✱✷✵✶✵✮ ❢♦r t❡st ❝♦♥str❛✐♥ts ✭❝♦♥t❡♥t ❛♥❞ s✐③❡ ♦❢ t❤❡ t❡st✱ ❢♦r ❡①❛♠♣❧❡✮✳ ❆ ❞❡s❝r✐♣t✐♦♥ ♦❢ t❤❡ t❡st ❞❡s✐❣♥✱ t❤❡ ❡♠♣❧♦②❡❞ st❛t✐st✐❝❛❧ ♠❡t❤♦❞s✱ st✉❞② r❡s✉❧ts ♦❢ ❛ r❡❛❧ ❛♣♣❧✐❝❛t✐♦♥ ♦❢ ❚❆■✲P■ t♦ ❣r❛❞✉❛t❡ st✉❞❡♥ts ❛r❡ ♣r❡s❡♥t❡❞ ✐♥ t❤✐s ✇♦r❦ ❛♥❞ t❤❡ ✈❛❧✐❞❛t✐♦♥ st✉❞✐❡s ♦❢ t❤❡ ♥❡✇ ♠❡t❤♦❞♦❧♦❣② ❢♦r ♣❛ss✴❢❛✐❧ ❝❧❛ss✐✜❝❛t✐♦♥✱ ❤✐❣❤❧✐❣❤t✐♥❣ t❤❡ ❣♦♦❞ q✉❛❧✐t② ♦❢ t❤❡ ♥❡✇ ❡✈❛❧✉❛t✐♦♥ s②st❡♠ ❛♥❞ ❡①❛♠✐♥❛t✐♦♥ ♦❢ ✐♠♣r♦✈❡♠❡♥t ✇✐t❤ t❤❡ ✉s❡ ♦❢ t❤❡ ♠❡t❤♦❞s ♦❢ ■❘❚ ❛♥❞ ❈❆❚✳
❑❡②✇♦r❞s✿ ❝♦♠♣✉t❡r✐③❡❞ ❛❞❛♣t✐✈❡ t❡st✱ ✐t❡♠ r❡s♣♦♥s❡ t❤❡♦r②✱ s❤❛❞♦✇ t❡st✳
❙✉♠ár✐♦
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s ✐①
▲✐st❛ ❞❡ ❋✐❣✉r❛s ①✐
▲✐st❛ ❞❡ ❚❛❜❡❧❛s ①✐✐✐
✶ ■♥tr♦❞✉çã♦ ✶
✷ ▼❡t♦❞♦❧♦❣✐❛ ❚❆■✲P■ ✺
✷✳✶ ◆ú♠❡r♦ ❞❡ ❝❛t❡❣♦r✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺
✷✳✷ ▼♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✸ ❊st✐♠❛çã♦ ❞♦ tr❛ç♦ ❧❛t❡♥t❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✹ ❙❡❧❡çã♦ ❞❡ ✐t❡♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾
✷✳✺ ❙❤❛❞♦✇ t❡st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵
✷✳✻ ❈r✐tér✐♦ ❞❡ ✐♥í❝✐♦ ❡ ♣❛r❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸ ❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ✶✸
✹ ❆♣❧✐❝❛çã♦ r❡❛❧ ✶✼
✺ ❊st✉❞♦s ❞❡ ❝❧❛ss✐✜❝❛çã♦ ✷✺
✻ ❈♦♥❝❧✉sõ❡s ✷✾
✻✳✶ ❙✉❣❡stõ❡s ♣❛r❛ P❡sq✉✐s❛s ❋✉t✉r❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾
❘❡❢❡rê♥❝✐❛s ❇✐❜❧✐♦❣rá✜❝❛s ✸✶
▲✐st❛ ❞❡ ❆❜r❡✈✐❛t✉r❛s
❚❖❊❋▲ ❚❡st ♦❢ ❊♥❣❧✐s❤ ❛s ❛ ❋♦r❡✐❣♥ ▲❛♥❣✉❛❣❡
■❊▲❚❙ ■♥t❡r♥❛t✐♦♥❛❧ ❊♥❣❧✐s❤ ▲❛♥❣✉❛❣❡ ❚❡st✐♥❣ ❙②st❡♠
❈P❊ ❈❡rt✐✜❝❛t❡ ♦❢ Pr♦✜❝✐❡♥❝② ✐♥ ❊♥❣❧✐s❤
❈❈▼❈ ❈✐ê♥❝✐❛s ❞❛ ❈♦♠♣✉t❛çã♦ ❡ ▼❛t❡♠át✐❝❛ ❈♦♠♣✉t❛❝✐♦♥❛❧
P■P●❊s Pr♦❣r❛♠❛ ■♥t❡r✐♥st✐t✉❝✐♦♥❛❧ ❞❡ Pós ●r❛❞✉❛çã♦ ❡♠ ❊st❛tíst✐❝❛
■❈▼❈ ■♥st✐t✉t♦ ❞❡ ❈✐ê♥❝✐❛s ▼❛t❡♠át✐❝❛s ❡ ❞❡ ❈♦♠♣✉t❛çã♦
❯❙P ❯♥✐✈❡rs✐❞❛❞❡ ❞❡ ❙ã♦ P❛✉❧♦
❯❋❙❈❛r ❯♥✐✈❡rs✐❞❛❞❡ ❋❡❞❡r❛❧ ❞❡ ❙ã♦ ❈❛r❧♦s
❊P■ ❊①❛♠❡ ❞❡ Pr♦✜❝✐ê♥❝✐❛ ❡♠ ■♥❣çês
❚❆■ ❚❡st❡ ❆❞❛♣t❛t✐✈♦ ■♥❢♦r♠❛t✐③❛❞♦
❚❘■ ❚❡♦r✐❛ ❞❡ ❘❡s♣♦st❛ ❛♦ ■t❡♠
●❘❊ ●r❛❞✉❛t❡ ❘❡❝♦r❞ ❊①❛♠✐♥❛t✐♦♥
❊❚❙ ❊❞✉❝❛t✐♦♥❛❧ ❚❡st✐♥❣ ❙❡r✈✐❝❡
❆❙❇❆❱ ❆r♠❡❞ ❙❡r✈✐❝❡s ❱♦❝❛t✐♦♥❛❧ ❆♣t✐t✉❞❡ ❚❡st ❇❛tt❡r②
❚❆■✲P■ ❚❡st❡ ❆❞❛♣t❛t✐✈♦ ■♥❢♦r♠❛t✐③❛❞♦ ❞❡ Pr♦✜❝✐ê♥❝✐❛ ❡♠ ■♥❣❧ês
▼P❆ ▼❡❞✐❞❛ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❆❞♠✐ssí✈❡❧
❈❆▲❊❆P✲❲❊❇ ❈♦♠♣✉t❡r✲❆✐❞❡❞ ▲❡❛r♥✐♥❣ ♦❢ ❊♥❣❧✐s❤ ❢♦r ❆❝❛❞❡♠✐❝ P✉r♣♦s❡s
▼❘● ▼♦❞❡❧♦ ❞❡ ❘❡s♣♦st❛ ●r❛❞✉❛❧
❊❆P ❊s♣❡r❛♥ç❛ ❛ P♦st❡r✐♦r✐
❈❆❚ ❈♦♠♣✉t❡r✐③❡❞ ❆❞❛♣t✐✈❡ ❚❡st
■❘❚ ■t❡♠ ❘❡s♣♦♥s❡ ❚❤❡♦r②
❈❈■ ❈✉r✈❛ ❈❛r❛❝t❡ríst✐❝❛ ❞♦ ■t❡♠
▲✐st❛ ❞❡ ❋✐❣✉r❛s
✶✳✶ ❉✐❛❣r❛♠❛ ❞❡ ✉♠ t❡st❡ ❛❞❛♣t❛t✐✈♦ ✐♥❢♦r♠❛t✐③❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷
✶✳✷ ❊①❡♠♣❧♦ ❞❡ ✉♠ ✐t❡♠ ❡ s✉❛ ♣♦ssí✈❡✐s ❛❧t❡r♥❛t✐✈❛s ❞❡ r❡s♣♦st❛s ♥♦ ❊P■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸
✶✳✸ ❚r✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦ ❞❛ ▼P❆ ❝♦♠ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛s ❛❧t❡r♥❛t✐✈❛s ❞❡ r❡s♣♦st❛s ❞❡ ❝❛❞❛ ✐t❡♠ ❞❛ ♣r♦✈❛ s✉♣♦♥❞♦ ❛ ❛❧t❡r♥❛t✐✈❛ ❆ ❝♦♠♦ ❛ ❝♦rr❡t❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✶✳✹ ❈r✐tér✐♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦♠ ❜❛s❡ ❡♠ ▼P❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹
✷✳✶ ❈✉r✈❛ ❈❛r❛❝t❡ríst✐❝❛ ❞♦ ■t❡♠ ✷✺ ❝♦♠ ❛s ✻ ❝❛t❡❣♦r✐❛s ✐♥✐❝✐❛✐s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✷ ❈✉r✈❛ ❈❛r❛❝t❡ríst✐❝❛ ❞♦ ■t❡♠ ✷✺ ❝♦♠ ❛❣r✉♣❛♠❡♥t♦ ❡♠ ✸ ❝❛t❡❣♦r✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻
✷✳✸ ❆❣r✉♣❛♠❡♥t♦ ❞❛s ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛ ❛♦s ✐t❡♥s ❛❞♦t❛❞♦ ♣❛r❛ ♦ ❚❆■✲P■✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼
✷✳✹ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ❝✉r✈❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛❝✉♠✉❧❛❞❛ s♦❜ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ❝♦♠ ✸ ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✺ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ❝✉r✈❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ❡s❝♦❧❤❛ ❞❛ ❝❛t❡❣♦r✐❛ s♦❜ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ❝♦♠ ✸ ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽
✷✳✻ ❘❡♣r❡s❡♥t❛ç❛♦ ❞♦ ❙❤❛❞♦✇ t❡st✳ ❋♦♥t❡✿ ✈❛♥ ❞❡r ▲✐♥❞❡♥✱ ✷✵✶✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶
✸✳✶ ❱❛❧♦r ✈❡r❞❛❞❡✐r♦ ❡♠ ❢✉♥çã♦ ❞♦ ✈❛❧♦r ❡st✐♠❛❞♦ ❞❡ θ ♣♦r ✸ ♣r✐♦r✐s✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s t❛♠❛♥❤♦s ❞❡ t❡st❡ ✭✷✵✱ ✷✺ ❡ ✸✵ ✐t❡♥s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✸✳✷ ❱í❝✐♦ ❞❡ ✶✵✵✵ r❡s♣♦♥❞❡♥t❡s s✐♠✉❧❛❞♦s ❡st✐♠❛❞♦ ♣♦r ✸ ♣r✐♦r✐s✱ ♣❛r❛ ❞✐❢❡r❡♥t❡s t❛♠❛✲ ♥❤♦s ❞❡ t❡st❡✭✷✵✱ ✷✺ ❡ ✸✵ ✐t❡♥s✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺
✹✳✶ ❇♦①♣❧♦t ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❡st✐♠❛❞❛ ❛♣ós ✷✺ ❡ ✹✵ ✐t❡♥s r❡s♣♦♥❞✐❞♦s ❞♦s ✺✾ ❛❧✉♥♦s ♥❛ ❛♣❧✐❝❛çã♦ ❞♦ ❚❆■✲P■✱ s❡♣❛r❛❞❛♠❡♥t❡ ♣❛r❛ ♦ ❣r✉♣♦ r❡♣r♦✈❛❞♦ ❡ ❛♣r♦✈❛❞♦ ♣❡❧♦ ❝r✐tér✐♦
▼P❆✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵
✹✳✷ Pr♦✜❝✐ê♥❝✐❛s ❡st✐♠❛❞❛s ❞♦ ❛❧✉♥♦ ✶✼ ❡♠ ❝❛❞❛ ♣❛ss♦ ❞♦ ❚❆■✲P■✱ ❛ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ r❡♣r❡s❡♥t❛ ❛ ❡st✐♠❛t✐✈❛ ✜♥❛❧ ❛♣ós ✹✵ ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶
✹✳✸ Pr♦✜❝✐ê♥❝✐❛s ❡st✐♠❛❞❛s ❞♦ ❛❧✉♥♦ ✷✻ ❡♠ ❝❛❞❛ ♣❛ss♦ ❞♦ ❚❆■✲P■✱ ❛ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ r❡♣r❡s❡♥t❛ ❛ ❡st✐♠❛t✐✈❛ ✜♥❛❧ ❛♣ós ✹✵ ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷
✹✳✹ Pr♦✜❝✐ê♥❝✐❛s ❡st✐♠❛❞❛s ❞♦ ❛❧✉♥♦ ✹✻ ❡♠ ❝❛❞❛ ♣❛ss♦ ❞♦ ❚❆■✲P■✱ ❛ ❧✐♥❤❛ ✈❡r♠❡❧❤❛ r❡♣r❡s❡♥t❛ ❛ ❡st✐♠❛t✐✈❛ ✜♥❛❧ ❛♣ós ✹✵ ✐t❡♥s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸
✺✳✶ ❈✉r✈❛ ❘❖❈ ♣❛r❛ ❛ ♣r♦✜❝✐ê♥❝✐❛ ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❝❧❛ss✐✜❝❛çã♦ ▼P❆ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺
✺✳✷ ❉❡♥s✐❞❛❞❡s ❡st✐♠❛❞❛s ♣❛r❛ ❛ ♣r♦✜❝✐ê♥❝✐❛ ♣♦r ❣r✉♣♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻
▲✐st❛ ❞❡ ❚❛❜❡❧❛s
✸✳✶ ❱í❝✐♦ ❞♦s ❡st✐♠❛❞♦r❡s ♣❛r❛ ❞✐❢❡r❡♥t❡s ♣r✐♦r✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✸✳✷ ❊rr♦ ◗✉❛❞rát✐❝♦ ▼é❞✐♦ ❞♦s ❡st✐♠❛❞♦r❡s ♣❛r❛ ❞✐❢❡r❡♥t❡s ♣r✐♦r✐s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹
✹✳✶ ❇❛♥❝♦ ❞❡ ✐t❡♥s ❞♦ ❚❆■✲P■✱ ♠❛✐♦ ❞❡ ✷✵✶✹ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽
✹✳✷ ❊st✐♠❛t✐✈❛s ❞♦s tr❛ç♦s ❧❛t❡♥t❡s ✭❛♣ós ✷✺ ❡ ✹✵ ✐t❡♥s r❡s♣♦♥❞✐❞♦s✮ ❡ ❝❧❛ss✐✜❝❛çã♦ ♣❡❧♦ ▼P❆ ♥❛ ❛♣❧✐❝❛ç❛♦ ❞♦ ❚❆■✲ ❞❡ ♠❛✐♦ ❞❡ ✷✵✶✹✳✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾
✹✳✸ P♦r❝❡♥t❛❣❡♠ ❞❡ ❛❝❡rt♦s ❞❡ ✹ ❛❧✉♥♦s ❡♠ ❝❛❞❛ ❝❛t❡❣♦r✐❛ ♥❛ ❛♣❧✐❝❛çã♦ ❞❡ ♠❛✐♦ ❞❡ ✷✵✶✹✳ ✷✵
✺✳✶ ❆❝✉rá❝✐❛ ♣❛r❛ ♦ ♣♦♥t♦ ❞❡ ❝♦rt❡ ♥♦ ❡st✉❞♦ ❞❡ s✐♠✉❛❧çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼
❈❛♣ít✉❧♦ ✶
■♥tr♦❞✉çã♦
❖ ❞♦♠í♥✐♦ ❞❛ ❧í♥❣✉❛ ✐♥❣❧❡s❛ ♣♦r ❛❧✉♥♦s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡♠ ❞✐✈❡rs❛s ár❡❛s ❞❛ ❝✐ê♥❝✐❛ é ❢✉♥❞❛✲ ♠❡♥t❛❧✱ t❛♥t♦ ♣❛r❛ ✉♠❛ ❛❞❡q✉❛❞❛ ❛❜s♦rçã♦ ❞♦ ❝♦♥t❡ú❞♦ ❞♦ ❝✉rs♦✱ q✉❛♥t♦ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ❞✐✈✉❧❣❛çã♦ ❞♦ tr❛❜❛❧❤♦ ❞❡ ♣❡sq✉✐s❛ r❡❛❧✐③❛❞♦✳ ◆❡st❡ ❝♦♥t❡①t♦✱ ♠✉✐t❛s ✐♥st✐t✉✐çõ❡s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ♥♦ ❇r❛s✐❧ ❡①✐❣❡♠ ✉♠❛ ❝♦♠♣r♦✈❛çã♦ ❞♦ ❞♦♠í♥✐♦ ❞♦ ✐♥❣❧ês ♣♦r s❡✉s ❛❧✉♥♦s✱ s❡❥❛ ♥♦ ❛t♦ ❞❡ ✐♥❣r❡ss♦ ♥♦ ♣r♦❣r❛♠❛✱ s❡❥❛ ❛♦ ❧♦♥❣♦ ❞❡ s❡✉ ❝✉rs♦✳
❍á ❞✐✈❡rs♦s ❡①❛♠❡s ❞❡ ❛❜r❛♥❣ê♥❝✐❛ ❡ r❡❝♦♥❤❡❝✐♠❡♥t♦ ✐♥t❡r♥❛❝✐♦♥❛✐s ♥♦r♠❛❧♠❡♥t❡ ❛❝❡✐t♦s✱ q✉❡ ❛t❡st❛♠ ❛ ♣r♦✜❝✐ê♥❝✐❛ ❡♠ ✐♥❣❧ês ♣❛r❛ ✐♥❞✐✈í❞✉♦s ♥ã♦✲♥❛t✐✈♦s✳ ❉❡♥tr❡ ♦s ♠❛✐s tr❛❞✐❝✐♦♥❛✐s✱ ♣♦❞❡♠♦s ❝✐t❛r ♦ ❚❡st ♦❢ ❊♥❣❧✐s❤ ❛s ❛ ❋♦r❡✐❣♥ ▲❛♥❣✉❛❣❡ ✭❚❖❊❋▲✮✱ ♦ ■♥t❡r♥❛t✐♦♥❛❧ ❊♥❣❧✐s❤ ▲❛♥❣✉❛❣❡ ❚❡st✐♥❣ ❙②st❡♠ ✭■❊▲❚❙✮ ❡ ♦ ❈❡rt✐✜❝❛t❡ ♦❢ Pr♦✜❝✐❡♥❝② ✐♥ ❊♥❣❧✐s❤ ✭❈P❊✮✳ ◆♦ ❡♥t❛♥t♦✱ ✉♠ ❞♦s ♠❛✐♦r❡s ✐♥❝♦♥✲ ✈❡♥✐❡♥t❡s ❞❡st❡s ❡①❛♠❡s é ♦ ❝✉st♦✱ q✉❡ ✈❛r✐❛ ❞❡ ✷✵✵ ❛ ✸✵✵ ❞ó❧❛r❡s ❛♠❡r✐❝❛♥♦s✱ ❛♣r♦①✐♠❛❞❛♠❡♥t❡✳ ■st♦ t♦r♥❛ ❛ s✉❛ ♦❜r✐❣❛t♦r✐❡❞❛❞❡ ✐♥❝♦❡r❡♥t❡ ❡♠ ✉♥✐✈❡rs✐❞❛❞❡s ♣ú❜❧✐❝❛s ❞❡ ♥♦ss♦ ♣❛ís✳ ❊ss❛ é ✉♠❛ ❞❛s ♣r✐♥❝✐♣❛✐s r❛③õ❡s ❞♦s ♣r♦❣r❛♠❛s ❞❡ ♣ós✲❣r❛❞✉❛çã♦ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❈♦♠♣✉t❛çã♦ ❡ ▼❛t❡♠át✐❛ ❈♦♠✲ ♣✉t❛❝✐♦♥❛❧ ✭❈❈▼❈✮ ❡ ❡♠ ❊st❛tíst✐❝❛ ✭P■P●❊s✮ ❞♦ ■❈▼❈✲❯❙P✱ s❡♥❞♦ ❡st❡ ú❧t✐♠♦ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛ ❯❋❙❈❛r✱ ♦❢❡r❡❝❡r❡♠ ✉♠ ❊①❛♠❡ ❞❡ Pr♦✜❝✐ê♥❝✐❛ ❡♠ ■♥❣❧ês ✭❊P■✮ ❝♦♠♦ ✉♠❛ ❛❧t❡r♥❛t✐✈❛ ❣r❛t✉✐t❛ ❛ s❡✉s ❛❧✉♥♦s✳
❆té ♦ ❛♥♦ ❞❡ ✷✵✶✸✱ ♦ ❊P■ ❡r❛ ❛♣❧✐❝❛❞♦ ♥♦ ❢♦r♠❛t♦ ❧á♣✐s✲❡✲♣❛♣❡❧ ❡ ❡st❡ tr❛❜❛❧❤♦ t❡♠ ❝♦♠♦ ♦❜❥❡t✐✈♦ t♦r♥á✲❧♦ ✉♠ t❡st❡ ❛❞❛♣t❛t✐✈♦ ✐♥❢♦r♠❛t✐③❛❞♦ ✭❚❆■✮✱ ♥♦ q✉❛❧ ♦s ✐t❡♥s sã♦ s❡❧❡❝✐♦♥❛❞♦s ❣r❛❞❛t✐✈❛♠❡♥t❡ ♣❛r❛ ♦ ✐♥❞✐✈í❞✉♦✱ ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛ ♣r♦✜❝✐ê♥❝✐❛✳ ❖ ✈❛❧♦r ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❞♦ ✐♥❞✐✈í❞✉♦ é ❛t✉❛❧✐③❛❞♦ ❛♣ós ❝❛❞❛ r❡s♣♦st❛✱ ❝♦♠ ❜❛s❡ ❡♠ ✉♠ ♠♦❞❡❧♦ ❞❛ ❚❡♦r✐❛ ❞❡ ❘❡s♣♦st❛ ❛♦ ■t❡♠ ✭❚❘■✮✳ ❆ss✐♠✱ ✐t❡♥s ♠✉✐t♦ ❢á❝❡✐s ♦✉ ♠✉✐t♦ ❞✐❢í❝❡✐s ♣❛r❛ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐♥❞✐✈í❞✉♦ ♥❡♠ ❝❤❡❣❛♠ ❛ s❡r ❛♣r❡s❡♥t❛❞♦s ❛ ❡❧❡✱ ❞✐♠✐♥✉✐♥❞♦ ♦ t❛♠❛♥❤♦ ❞♦ t❡st❡✱ s❡✉ t❡♠♣♦ ❞❡ r❡❛❧✐③❛çã♦ ❡ t♦r♥❛♥❞♦✲♦ ♠❛✐s ❡✜❝✐❡♥t❡✱ ♦❜❥❡t✐✈♦ ❡
❝♦♠ r❡s✉❧t❛❞♦ ✐♠❡❞✐❛t♦ ✭❲❡✐ss✱✶✾✽✷✮✳ ◆❛ ❋✐❣✉r❛✶✳✶sã♦ ❛♣r❡s❡♥t❛❞♦s ♦s ♣r♦❝❡❞✐♠❡♥t♦s ❞❡ s❡❧❡çã♦ ❡
❛❞♠✐♥✐str❛çã♦ ❞❡ ✐t❡♥s ♥♦ t❡st❡ ❡ ❛t✉❛❧✐③❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❛s ♣r♦✜❝✐ê♥❝✐❛s✱ ✐t❡r❛t✐✈❛♠❡♥t❡✱ ❛té q✉❡ ❛❧❣✉♠ ❝r✐tér✐♦ ❞❡ ♣❛r❛❞❛ s❡❥❛ s❛t✐s❢❡✐t♦✳
✷ ■◆❚❘❖❉❯➬➹❖ ✶✳✵
❋✐❣✉r❛ ✶✳✶✿ ❉✐❛❣r❛♠❛ ❞❡ ✉♠ t❡st❡ ❛❞❛♣t❛t✐✈♦ ✐♥❢♦r♠❛t✐③❛❞♦
❆❧é♠ ❞❛s ✈❛♥t❛❣❡♥s ❛❝✐♠❛ ♠❡♥❝✐♦♥❛❞❛s✱ ♦s t❡st❡s ❛❞❛♣t❛t✐✈♦s ✐♥❢♦r♠❛t✐③❛❞♦s ✭❚❆■✮✱ ❡♠ ❝♦♠❜✐✲ ♥❛çã♦ ❝♦♠ ❛ ❚❘■✱ ♣♦ss✐❜✐❧✐t❛♠ ♦ ❝á❧❝✉❧♦ ❞❡ ♣r♦✜❝✐ê♥❝✐❛s ❝♦♠♣❛rá✈❡✐s ❡♥tr❡ ✐♥❞✐✈í❞✉♦s q✉❡ r❡s♣♦♥✲
❞❡r❛♠ ❝♦♥❥✉♥t♦s ❞✐❢❡r❡♥t❡s ❞❡ ✐t❡♥s✱ ❡ ❡♠ ♠♦♠❡♥t♦s ❞✐❢❡r❡♥t❡s ✭❲❛✐♥❡r ❡t ❛❧✳✱ ✷✵✵✵✮✳ ■st♦ ❢❛❝✐❧✐t❛
❜❛st❛♥t❡ ❛ ❛✈❛❧✐❛çã♦ ❞❡ ❝♦♥str✉t♦s ❡♠ ❧❛r❣❛ ❡s❝❛❧❛✱ r❡s✉❧t❛♥❞♦ ♥♦ s❡✉ ✉s♦ ❡♠ ✐♠♣♦rt❛♥t❡s ❡①❛♠❡s✱
t❛✐s ❝♦♠♦ ●r❛❞✉❛t❡ ❘❡❝♦r❞ ❊①❛♠✐♥❛t✐♦♥ ✭●❘❊✮ ✭❇r✐❞❣❡♠❛♥ ✫ ❈❧✐♥❡✱ ✷✵✵✵❀❊✐❣♥♦r✱ ✶✾✾✸✮ ✱ ❞❡s❡♥✲
✈♦❧✈✐❞♦ ♣❡❧♦ ❊❞✉❝❛t✐♦♥❛❧ ❚❡st✐♥❣ ❙❡r✈✐❝❡ ✭❊❚❙✮ ❡♠ ✶✾✾✻❀ ❚❡st ♦❢ ❊♥❣❧✐s❤ ❛s ❛ ❋♦r❡✐❣♥ ▲❛♥❣✉❛❣❡
✭❚❖❊❋▲✮✭❊✐❣♥♦r ❡t ❛❧✳✱✶✾✾✽❀❑✐rs❝❤ ❡t ❛❧✳✱✶✾✾✽❀❲❛✐♥❡r ✫ ❲❛♥❣✱✷✵✵✵✮✱ t❛♠❜é♠ ❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧♦
❊❚❙❀ ❆r♠❡❞ ❙❡r✈✐❝❡s ❱♦❝❛t✐♦♥❛❧ ❆♣t✐t✉❞❡ ❚❡st ❇❛tt❡r② ✭❆❙❇❆❱✮✭❙❛♥❞s ❡t ❛❧✳✱ ✶✾✾✼❀ ❙❡❣❛❧❧✱✶✾✾✸✮✱
❞❡s❡♥✈♦❧✈✐❞♦ ♣❡❧♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❉❡❢❡s❛ ❞♦s ❊st❛❞♦s ❯♥✐❞♦s ♣❛r❛ s❡❧❡❝✐♦♥❛r ♣♦t❡♥❝✐❛✐s r❡❝r✉t❛s ♣❛r❛ ♦ s❡r✈✐ç♦ ♠✐❧✐t❛r✳
P❛r❛ ❥✉st✐✜❝❛r ❛ ❡s❝♦❧❤❛ ❞❛ ♠❡t♦❞♦❧♦❣✐❛ ❡st❛tíst✐❝❛ ❛❞♦t❛❞❛ ♥❡st❡ tr❛❜❛❧❤♦✱ ❛♣r❡s❡♥t❛♠♦s ❛ s❡❣✉✐r ♦ ❢♦r♠❛t♦ ❝♦♠ q✉❡ ♦ ❊P■ ❢♦✐ ❛♣❧✐❝❛❞♦ ♥♦ ♣r♦❣r❛♠❛ ❈❈▼❈ ❡♥tr❡ ✷✵✵✷ ❡ ✷✵✶✸✱ s❡r✈✐♥❞♦ ❝♦♠♦ ✉♠ ❛❧✐❝❡r❝❡❡ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞♦ ❚❡st❡ ❆❞❛♣t❛t✐✈♦ ■♥❢♦r♠❛t✐③❛❞♦ ❞❡ Pr♦✜❝✐ê♥❝✐❛ ❡♠ ■♥❣❧ês ✭❚❆■✲P■✮✳
❉❡s❞❡ ♦ ❛♥♦ ✷✵✵✷✱ ♦ ❊P■ ❝♦♥s✐st❡ ❡♠ ✉♠❛ ♣r♦✈❛ ❝♦♠♣♦st❛ ♣♦r ✐t❡♥s ❞❡ ♠ú❧t✐♣❧❛ ❡s❝♦❧❤❛✱ ❛♣❧✐❝❛❞❛ s❡♠❡str❛❧♠❡♥t❡ ❡♠ ❢♦r♠❛t♦ ❧á♣✐s✲❡✲♣❛♣❡❧✳ P❛r❛ ❛ ❝♦♥❢❡❝çã♦ ❞❛ ♣r♦✈❛✱ s❡❧❡❝✐♦♥❛♠✲s❡ ❞❡ ✷✺ ❛ ✸✵ ✐t❡♥s ❞❡ ✉♠ ❜❛♥❝♦ ❝♦♠ ✶✻✼ ✐t❡♥s ♥♦ t♦t❛❧✱ s✉❜❞✐✈✐❞✐❞♦s ❡♠ ✸ ♠ó❞✉❧♦s ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿
✶✳ ◆♦ ♠ó❞✉❧♦ ✶ sã♦ ❛♣r❡s❡♥t❛❞♦s r❡s✉♠♦s ❞❡ ❛rt✐❣♦s ❞❡ ♣❡r✐ó❞✐❝♦s ❞❛s ár❡❛s ❞❡ ❈♦♠♣✉t❛çã♦✱ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❡ ❊st❛tíst✐❝❛ ❡ ♣❡r❣✉♥t❛s s♦❜r❡ s❡✉s ❝♦♠♣♦♥❡♥t❡s ❞❡ ❡str✉t✉r❛ ❝✐❡♥✲ tí✜❝❛✳
✷✳ ◆♦ ♠ó❞✉❧♦ ✷ t❡♠✲s❡ ✉♠ tr❡❝❤♦ ❞❛ ✐♥tr♦❞✉çã♦ ❞❡ ✉♠ ❛rt✐❣♦ ❝✐❡♥tí✜❝♦✱ ❞❛s ♠❡s♠❛s ár❡❛s✱ ❡ ♣❡r❣✉♥t❛s ✭❡♠ ♣♦rt✉❣✉ês✮ s♦❜r❡ ❝♦♠♣r❡❡♥sã♦ ❞♦ t❡①t♦ ❡ r❡❧❛çã♦ ❡♥tr❡ ✐❞❡✐❛s ❝♦♥t✐❞❛s ♥❡❧❡✳ ✸✳ ◆♦ ♠ó❞✉❧♦ ✸ ❛s ♣❡r❣✉♥t❛s ❡stã♦ r❡❧❛❝✐♦♥❛❞❛s ❛ ❝♦♥✈❡♥çõ❡s ❞❛ ❧í♥❣✉❛ ✐♥❣❧❡s❛✱ t❛✐s ❝♦♠♦
❝♦♥❥✉♥çõ❡s✱ t❡♠♣♦s ✈❡r❜❛✐s✱ r❡❧❛t✐✈❡ ❝❧❛✉s❡s ❡ ❛rt✐❣♦s✳
❖s ✐t❡♥s ❞♦ ❜❛♥❝♦ ❢♦r❛♠ ❡❧❛❜♦r❛❞♦s✱ ♥❛ é♣♦❝❛✱ ♣♦r ❆♥❞r❡❛ ❏❡ss✐❝❛ ❇♦r❣❡s ▼♦♥③ó♥✱ ❛t✉❛❧ ❞♦❝❡♥t❡ ❞♦ ■♥st✐t✉t♦ ❋❡❞❡r❛❧ ❞♦ ❘✐♦ ●r❛♥❞❡ ❞♦ ❙✉❧✱ ❡♠ ❝♦♥❥✉♥t♦ ❝♦♠ ❛ ♣r♦❢❡ss♦r❛ ❙❛♥❞r❛ ▼❛r✐❛ ❆❧✉ís✐♦✱ ❞♦
✶✳✵ ✸
❜❛s❡♦✉✲s❡ ♥❛ t❛①♦♥♦♠✐❛ ❞❡ ❇❧♦♦♠ ✭❇❧♦♦♠✱ ✶✾✽✹✮✱ ♦❜❥❡t✐✈❛♥❞♦ ❛✈❛❧✐❛r ❛ ❝♦♠♣❡tê♥❝✐❛ ♥❛ ❧❡✐t✉r❛ ❡
❝♦♠♣r❡❡♥sã♦ ❞❡ ❛rt✐❣♦s ❝✐❡♥tí✜❝♦s ❞❛s ár❡❛s ❞❡ ❈♦♠♣✉t❛çã♦✱ ▼❛t❡♠át✐❝❛ ❆♣❧✐❝❛❞❛ ❡ ❊st❛tíst✐❝❛✳ ❈♦♠ ♦ ✐♥t✉✐t♦ ❞❡ ♠✐♥✐♠✐③❛r ❛ ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ ✏❝❤✉t❡✧❞❛ r❡s♣♦st❛ ❝♦rr❡t❛ ❡ ❞❡ ♥ã♦ ♣r❡ss✉♣♦r q✉❡ ♦ ❝♦♥❤❡❝✐♠❡♥t♦ ❞♦ ❛❧✉♥♦ s♦❜r❡ ✉♠ ❞❡t❡r♠✐♥❛❞♦ ✐t❡♠ é ❛♣❡♥❛s ❜✐♥ár✐♦ ✭❝♦rr❡t♦ ♦✉ ✐♥❝♦rr❡t♦✮✱ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❛ r❡s♣♦st❛ ❞♦ ❛❧✉♥♦ s❡❣✉❡ ❛ ♠❡t♦❞♦❧♦❣✐❛ ❞❛ ▼❡❞✐❞❛ ❞❡ Pr♦❜❛❜✐❧✐❞❛❞❡ ❆❞♠✐ssí✈❡❧
✭▼P❆✮ ✭❑❧✐♥❣❡r✱✶✾✾✼✮✳ ❆ ❋✐❣✉r❛✶✳✷✐❧✉str❛ ❛s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ r❡s♣♦st❛ ❞♦ ❛❧✉♥♦ ❛ ✉♠ ✐t❡♠ ❞♦ ❊P■✳
❙ã♦ três ❛s ❛❧t❡r♥❛t✐✈❛s ❞❡ r❡s♣♦st❛ ❡♠ ❝❛❞❛ ✐t❡♠ ❞❡ ♠ú❧t✐♣❧❛ ❡s❝♦❧❤❛ ✭❆✱ ❇ ❡ ❈✮✱ r❡♣r❡s❡♥t❛❞❛s ♥♦s ✈ért✐❝❡s ❞❡ ✉♠ tr✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦✱ s❡♥❞♦ ❛♣❡♥❛s ✉♠❛ ❞❡❧❛s ❛ ❝♦rr❡t❛✱ ♥♦ ❡♥t❛♥t♦✱ ♦ ❛❧✉♥♦ ♣♦ss✉✐ ✶✸ ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ r❡s♣♦st❛✱ q✉❡ ❡①♣r❡ss❛♠ ♦ s❡✉ ❣r❛✉ ❞❡ ❝❡rt❡③❛ s♦❜r❡ q✉❛❧ ❞❛s ✸ ❛✜r♠❛t✐✈❛s é ❛ ❝♦rr❡t❛✳ ◗✉❡ ♣♦❞❡♠ s❡r s❡❧❡❝✐♦♥❛❞❛s ❞❛ ♠❛♥❡✐r❛ ❛ s❡❣✉✐r✿
• ❙❡ ❡st✐✈❡r t♦t❛❧♠❡♥t❡ ❝❡rt♦✴s❡❣✉r♦ ✉s❡ ❛s ♦♣çõ❡s ❆✱ ❇ ♦✉ ❈✳
• ❙❡ ❡st✐✈❡r t♦t❛❧♠❡♥t❡ ✐♥❝❡rt♦✴✐♥s❡❣✉r♦ ✉s❡ ❛ ♦♣çã♦ ▼✳
• ❙❡ ✉♠❛ ❞❛s ♦♣çõ❡s ❆✱ ❇✱ ❈ ♣❛r❡❝❡ ❞❡✜♥✐t✐✈❛♠❡♥t❡ ❡rr❛❞♦✱ ❡s❝♦❧❤❛ ❡♥tr❡ ❛s ✺ ♦♣çõ❡s ❞❛ ❧✐♥❤❛
♦♣♦st❛✳
• ■♥❞✐q✉❡ ♣r❡❢❡rê♥❝✐❛ ❡♥tr❡ ❞✉❛s ♦♣çõ❡s ❆✱ ❇ ♦✉ ❈ ❡s❝♦❧❤❡♥❞♦ ❛s ♦♣çõ❡s ❉✱ ❋✱ ●✱ ■✱ ❏ ♦✉ ▲✳
• ❙❡ ❞✉❛s ♦♣çõ❡s ❆✱ ❇✱ ♦✉ ❈ ♣❛r❡❝❡♠ ✐❣✉❛✐s ❡s❝♦❧❤❛ ❛s ♦♣çõ❡s ❊✱ ❍ ♦✉ ❑ ✳
❋✐❣✉r❛ ✶✳✷✿ ❊①❡♠♣❧♦ ❞❡ ✉♠ ✐t❡♠ ❡ s✉❛ ♣♦ssí✈❡✐s ❛❧t❡r♥❛t✐✈❛s ❞❡ r❡s♣♦st❛s ♥♦ ❊P■✳
◆❛ ❋✐❣✉r❛ ✶✳✸t❡♠✲s❡ ❛ ❝❧❛ss✐✜❝❛çã♦ ❞❛ r❡s♣♦st❛ ❞♦ ❛❧✉♥♦ ❞❡ ❛❝♦r❞♦ ❝♦♠ s✉❛ ❡s❝♦❧❤❛ ❡♠✿ t♦t❛❧✲
♠❡♥t❡ ✐♥❢♦r♠❛❞♦✱ ✐♥❢♦r♠❛❞♦✱ ♣❛r❝✐❛❧♠❡♥t❡ ✐♥❢♦r♠❛❞♦✱ ♠❛❧ ✐♥❢♦r♠❛❞♦✱ t♦t❛❧♠❡♥t❡ ♠❛❧ ✐♥❢♦r♠❛❞♦ ❡
✹ ■◆❚❘❖❉❯➬➹❖ ✶✳✵
❋✐❣✉r❛ ✶✳✸✿ ❚r✐â♥❣✉❧♦ ❡q✉✐❧át❡r♦ ❞❛ ▼P❆ ❝♦♠ ❛ ❝❛r❛❝t❡r✐③❛çã♦ ❞❛s ❛❧t❡r♥❛t✐✈❛s ❞❡ r❡s♣♦st❛s ❞❡ ❝❛❞❛ ✐t❡♠ ❞❛ ♣r♦✈❛ s✉♣♦♥❞♦ ❛ ❛❧t❡r♥❛t✐✈❛ ❆ ❝♦♠♦ ❛ ❝♦rr❡t❛✳
❖ ❛❧✉♥♦ é ❛♣r♦✈❛❞♦ s❡ ♦ ♣❡r❝❡♥t✉❛❧ ❞❡ r❡s♣♦st❛s ❝❧❛ss✐✜❝❛❞❛s ❝♦♠♦ ✏t♦t❛❧♠❡♥t❡ ✐♥❢♦r♠❛❞♦✧❢♦r ♠❛✐♦r ♦✉ ✐❣✉❛❧ ❛ ✺✵✪ ❡ s❡ ♦ ♣❡r❝❡♥t✉❛❧ ❞❡ r❡s♣♦st❛s ✏t♦t❛❧♠❡♥t❡ ♠❛❧ ✐♥❢♦r♠❛❞♦✧❢♦r ♠❡♥♦r ♦✉ ✐❣✉❛❧ ❛ ✷✺✪ ♦✉ s❡ ✾✵✪ ♦✉ ♠❛✐s ❞❡ r❡s♣♦st❛s ❡st✐✈❡r❡♠ ♥❛s ❝❧❛ss❡s ✏t♦t❛❧♠❡♥t❡ ✐♥❢♦r♠❛❞♦✧✱ ✏✐♥❢♦r♠❛❞♦✧❡ ✏♣❛r❝✐❛❧♠❡♥t❡ ✐♥❢♦r♠❛❞♦✧❡ ✶✵✪ ♦✉ ♠❡♥♦s ❞❡ r❡s♣♦st❛s ♥❛ ❝❧❛ss❡ ✏t♦t❛❧♠❡♥t❡ ♠❛❧ ✐♥❢♦r♠❛❞♦✧✱ ❝♦♥✲
❢♦r♠❡ ❋✐❣✉r❛ ✶✳✹✳ P❛r❛ ♦s ❛❧✉♥♦s ♥ã♦ ❛♣r♦✈❛❞♦s s❡❣✉♥❞♦ ❡ss❡ ❝r✐tér✐♦✱ ♠❛s q✉❛s❡ ❛♣r♦✈❛❞♦s s❡ ♥ã♦
❢♦ss❡♠ ❛s r❡s♣♦st❛s ❞❡ ✉♠ ♦✉ ❞♦✐s ✐t❡♥s ✭♥♦ ♠á①✐♠♦✮✱ ✉♠ ❝r✐tér✐♦ ❛❧t❡r♥❛t✐✈♦ é ❞✐s♣♦♥✐❜✐❧✐③❛❞♦
❝♦♥s✐❞❡r❛♥❞♦✲s❡ ❛♣❡♥❛s ♦ ♠ó❞✉❧♦ ✶✱✏❊str✉t✉r❛ ❞❡ ❚❡①t♦s ❈✐❡♥tí✜❝♦s✧✭❋✐❣✉r❛ ✶✳✹✮✳
❋✐❣✉r❛ ✶✳✹✿ ❈r✐tér✐♦ ❞❡ ❝❧❛ss✐✜❝❛çã♦ ❝♦♠ ❜❛s❡ ❡♠ ▼P❆✳
❈❛♣ít✉❧♦ ✷
▼❡t♦❞♦❧♦❣✐❛ ❚❆■✲P■
❖ ❚❆■✲P■ ❢♦✐ ❞❡s❡♥✈♦❧✈✐❞♦ ❡♠ ❏❛✈❛ ✶✳✼✳✵ ❡ ❙◗▲✐t❡ ✈❡rsã♦ ✸✳✼✳✷ ✭▲❛♥s✱✷✵✵✻✮✱ ♣❛r❛ ❛r♠❛③❡♥❛♠❡♥t♦
❞♦ ❜❛♥❝♦ ❞❡ ❞❛❞♦s✳
❖ ♣r♦❣r❛♠❛ ❙❛♠❡✲❈❆❚✱ ❝r✐❛❞♦ ♣♦r ❚❤❛❧❡s ❆❦✐r❛ ▼✳ ❘✐❝❛rt❡ ❛♦ ❧♦♥❣♦ ❞❡ s❡✉ ♣r♦❣r❛♠❛ ❞❡ ♠❡str❛❞♦✱ ✜♥❛❧✐③❛❞♦ ❡♠ ✷✵✶✷ ♣❡❧♦ ❈❈▼❈✲■❈▼❈✱ ❢♦✐ ✉s❛❞♦ ❝♦♠♦ ❜❛s❡ ♣❛r❛ ❛ ❝♦♥str✉çã♦ ❞♦ ❚❆■✲ P■ ✭❘✐❝❛rt❡✱ ✷✵✶✸✮✳ ❖ ❙❛♠❡✲❈❆❚ é ✉♠ ♣r♦❣r❛♠❛ q✉❡ ♣❡r♠✐t❡ ❛ ❛♣❧✐❝❛çã♦ ❞❡ t❡st❡s ❛❞❛♣t❛t✐✈♦s ✐♥❢♦r♠❛t✐③❛❞♦s✱ ❝♦♠ ✐t❡♥s ❞♦ ❜❛♥❝♦ ❝❛❧✐❜r❛❞♦s ❞❡ ❛❝♦r❞♦ ❝♦♠ ♦ ♠♦❞❡❧♦ ❞❡ r❡s♣♦st❛ ❣r❛❞✉❛❧ ❞❡ ❙❛♠❡❥✐♠❛ ✭✶✾✻✾✮ ❞❛ ❚❘■✱ ❝r✐tér✐♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ♣❛r❛ s❡❧❡çã♦ ❞❡ ✐t❡♥s ❛ ❝❛❞❛ ♣❛ss♦ ❞♦ t❡st❡✱ ❡st✐♠❛çã♦ ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ♣❡❧♦ ♠ét♦❞♦ ❜❛②❡s✐❛♥♦ ❞❡ ❡s♣❡r❛♥ç❛ ❛ ♣♦st❡r✐♦r✐ ❡ ❝♦♠ ❛❜♦r❞❛❣❡♠ ❙❤❛❞♦✇ t❡st ♣❛r❛ ✐♠♣♦s✐çã♦ ❞❡ r❡str✐çõ❡s✳
❆ ✈❡rsã♦ ❛t✉❛❧ ❞♦ ❚❆■✲P■ ❝♦♥t♦✉ ❝♦♠ ❛ ❝♦❧❛❜♦r❛çã♦ ❞♦ ❛❧✉♥♦ ❞♦ ❇❛❝❤❛r❡❧❛❞♦ ❡♠ ❈✐ê♥❝✐❛s ❞❛ ❈♦♠♣✉t❛çã♦ ❞♦ ■❈▼❈✱ ▲❡♦♥❛r❞♦ ❚❛❞❛s❤✐ ▼②✐❛❦❡✱ ♣❛r❛ ❛ ✐♥❝❧✉sã♦ ❞❡ ❛❧❣✉♠❛s ❢❛❝✐❧✐❞❛❞❡s ♥❛ ✐♥t❡r❛çã♦ ✉s✉ár✐♦✲♠áq✉✐♥❛✳
◆❛ ❙❡çã♦ ✷✳✶✱ ❛♣r❡s❡♥t❛♠♦s ♦s ❡st✉❞♦s r❡❛❧✐③❛❞♦s ♣❛r❛ ❛ ❞❡✜♥✐çã♦ ❞❡ q✉❛♥t❛s ❝❛t❡❣♦r✐❛s ❞❡ r❡s✲
♣♦st❛s s❡rã♦ ❝♦♥s✐❞❡r❛❞❛s ♥♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛✳ ◆❛ ❙❡çã♦✷✳✷✱ é ❞❡✜♥✐❞♦ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛✳
◆❛ ❙❡çã♦ ✷✳✸❞❡s❝r❡✈❡♠♦s ♦ ♠ét♦❞♦ ❞❡ ❡st✐♠❛çã♦ ♣❛r❛ ❛s ❤❛❜✐❧✐❞❛❞❡s ❞♦ ❚❆■✲P■✳ ❆ ❙❡çã♦ ✷✳✹tr❛③
♦ ♠ét♦❞♦ ❞❡ s❡❧❡çã♦ ❞❡ ✐t❡♥s ♣❛r❛ ♦ t❡st❡ ❛❞❛♣t❛t✐✈♦✳ ❆ ❙❡çã♦✷✳✺❛♣r❡s❡♥t❛ ♦ ♠ét♦❞♦ ❙❤❛❞♦✇ ❚❡st
♣❛r❛ ✐♠♣♦s✐çã♦ ❞❡ r❡str✐çõ❡s ❞❡ss❛ s❡❧❡çã♦✳ ❋✐♥❛❧♠❡♥t❡✱ ❛ ❙❡çã♦✷✳✻❞❡s❝r❡✈❡ ♦s ❝r✐tér✐♦s ❞❡ ✐♥í❝✐♦ ❡
♣❛r❛❞❛ ❞♦ t❡st❡✳
✷✳✶ ◆ú♠❡r♦ ❞❡ ❝❛t❡❣♦r✐❛s
❆s ♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ r❡s♣♦st❛ ❛ ❝❛❞❛ ✐t❡♠ ❞♦ ❊P■ ♣♦❞❡♠ s❡r ❝♦♥s✐❞❡r❛❞❛s ♦r❞✐♥❛✐s ❝♦♠ ✶✸
♣♦ss✐❜✐❧✐❞❛❞❡s ❞❡ r❡s♣♦st❛s ❝❧❛ss✐✜❝❛❞❛s ❡♠ ✻ ❝❛t❡❣♦r✐❛s ❞❡ ❛❝♦r❞♦ ❝♦♠ ❛ ❋✐❣✉r❛✶✳✸✳ ❈♦♠♦ ♦ ✐♥t✉✐t♦
❞❡st❡ tr❛❜❛❧❤♦ é ❛♣r✐♠♦r❛r ♦ ❊P■ ♠❛♥t❡♥❞♦ ❡ ❛♣r♦✈❡✐t❛♥❞♦ ♦ ♠á①✐♠♦ ♣♦ssí✈❡❧ s✉❛ ❤✐stór✐❛✱ ♦ ♠♦❞❡❧♦ ❞❡ r❡s♣♦st❛ ❣r❛❞✉❛❧ ✭▼❘●✮✱ ♣r♦♣♦st♦ ♣♦r ❙❛♠❡❥✐♠❛ ✭✶✾✻✾✮✱ ❢♦✐ ❛❞♦t❛❞♦ ♣❛r❛ ♦ ❚❆■✲P■✳ ◆♦ ❡♥t❛♥t♦✱ ✉♠❛ ❛♥á❧✐s❡ ❞❡s❝r✐t✐✈❛ ❡ ✐♥❢❡r❡♥❝✐❛❧ s♦❜r❡ ♦ ♥ú♠❡r♦ ❞❡ ❝❛t❡❣♦r✐❛s ❛ s❡r ❝♦♥s✐❞❡r❛❞♦ ❛♣♦♥t♦✉ ♣❛r❛ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ r❡❞✉çã♦ ❛ ✸ ♣♦ss✐✈❡✐s r❡s♣♦st❛s ❡♠ ❝❛❞❛ ✐t❡♠✳
❊ss❛ ❞❡❝✐sã♦ ❢♦✐ ❜❛s❡❛❞❛ ♥❛s ❛♥á❧✐s❡s ❞❡ ✉♠❛ ♣❛rt❡ ❞♦s ✶✻✼ ✐t❡♥s ❝r✐❛❞♦s ❡ ❛♣❧✐❝❛❞♦s ♥♦ ♣❡r✐♦❞♦ ❞❡ ✷✵✵✷ ❛ ✷✵✶✷ ♥♦ ❊P■ ❢♦r♠❛t♦ ❧á♣✐s✲❡✲♣❛♣❡❧✱ ♦s q✉❛✐s ❢♦r❛♠ ✜❧tr❛❞♦s ✼✹ ✐t❡♥s ♣❛r❛ ❛ ❝❛❧✐❜r❛çã♦ ❞♦s ♣❛râ♠❡tr♦s q✉❡ t✐♥❤❛♠ ❛♦ ♠❡♥♦s ✽✵ r❡s♣♦♥❞❡♥t❡s ❛♦ ❧♦♥❣♦ ❞♦ t❡♠♣♦ ✭♣❛r❛ ♦❜t❡r❡♠✲s❡ ❡st✐♠❛t✐✈❛s r❡❧❛t✐✈❛♠❡♥t❡ ❝♦♥✜á✈❡✐s ❞♦s ♣❛râ♠❡tr♦s✮ ❡ ♣r❡s❡♥t❡s ❡♠ ♣r♦✈❛s ❝♦♠✉♥s ✭♣❛r❛ ❣❛r❛♥t✐r ❛ ❡q✉❛❧✐③❛çã♦ s✐♠✉❧tâ♥❡❛ ❝♦♠ ❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦❞❡❧♦ ❞❛ ❚❘■✮✱ ♥♦ ❡♥t❛♥t♦ ❞❡✈✐❞♦ ❛♦ ♣❡q✉❡♥♦ t❛♠❛♥❤♦ ❛♠♦str❛❧✱ ❛❧❣✉♠❛s ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛s ♥ã♦ t✐♥❤❛♠ ❢r❡q✉ê♥❝✐❛s s✉✜❝✐❡♥t❡ ♣❛r❛ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ❞❡ ✐t❡♥s✳
❏✉♥t❛♥❞♦ ✐ss♦ ❝♦♠ ❛ ❛♥á❧✐s❡ ❡①♣❧♦r❛tór✐❛ ❞❛s ❝✉r✈❛s ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ✐t❡♠ ✭❈❈■✮✱ ❞❡❝✐❞✐✉✲s❡
❥✉♥t❛s ❛s r❡s♣♦st❛s ❡♠ ✸ ❝❛t❡❣♦r✐❛s✱ ◆❛s ❋✐❣✉r❛s ✷✳✶ ❡ ✷✳✷ sã♦ ❛♣r❡s❡♥t❛❞♦s ❛s ❈❈■ ❞♦ ✐t❡♠ ✷✺
❛♥t❡s ❡ ❞❡♣♦✐s ❞♦ ❛❣r✉♣❛♠❡♥t♦ ❞❡ ❝❛t❡❣♦r✐❛s✳
✻ ▼❊❚❖❉❖▲❖●■❆ ❚❆■✲P■ ✷✳✶
❋✐❣✉r❛ ✷✳✶✿ ❈✉r✈❛ ❈❛r❛❝t❡ríst✐❝❛ ❞♦ ■t❡♠ ✷✺ ❝♦♠ ❛s ✻ ❝❛t❡❣♦r✐❛s ✐♥✐❝✐❛✐s
❋✐❣✉r❛ ✷✳✷✿ ❈✉r✈❛ ❈❛r❛❝t❡ríst✐❝❛ ❞♦ ■t❡♠ ✷✺ ❝♦♠ ❛❣r✉♣❛♠❡♥t♦ ❡♠ ✸ ❝❛t❡❣♦r✐❛s
✷✳✷ ▼❖❉❊▲❖ ❉❊ ❙❆▼❊❏■▼❆ ✼
❋✐❣✉r❛ ✷✳✸✿ ❆❣r✉♣❛♠❡♥t♦ ❞❛s ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛ ❛♦s ✐t❡♥s ❛❞♦t❛❞♦ ♣❛r❛ ♦ ❚❆■✲P■✳
✷✳✷ ▼♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛
❙✉♣♦♥❤❛ k = 0,1,2 ❞❡♥♦t❛♥t♦ ❛s ✸ ❝❛t❡❣♦r✐❛s ❞❛ ❋✐❣✉r❛ ✷✳✸ ❝❛t❡❣♦r✐❛s ♦r❣❛♥✐③❛❞❛s ❡♠ ♦r❞❡♠
❝r❡s❝❡♥t❡✱ ♦✉ s❡❥❛✱ q✉❛♥t♦ ♠❛✐♦r ♦ ✈❛❧♦r ❞❡ ❦✱ ♠❛✐s ♣ró①✐♠❛ ❡❧❛ ❡st❛rá ❞❛ r❡s♣♦st❛ t♦t❛❧♠❡♥t❡ ❝♦rr❡t❛✳
❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈í❞✉♦✱ ❝♦♠ ✈❛❧♦r ❞❡ ♣r♦✜❝✐ê♥❝✐❛ θ✱ ❡s❝♦❧❤❡r ❛ ❝❛t❡❣♦r✐❛ ❦ ♦✉ ❛❧❣✉♠❛
♠❛✐♦r q✉❡ ❡❧❛ ♥♦ ✐t❡♠ ✐ é ❞❛❞❛ ♣♦r✿
Pi,k+(θ) = 1
1 +exp[−ai(θ−bi,k)]
, ✭✷✳✶✮
s❡♥❞♦ bi,k ♦ ♣❛râ♠❡tr♦ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ❞❛ ❝❛t❡❣♦r✐❛ k ❞♦ ✐t❡♠ ✐✱ Pi,+0 = 1 ❡ ai ♦ ♣❛râ♠❡tr♦ ❞❡
❞✐✜❝✉❧❞❛❞❡ ❞♦ ✐t❡♠i✳ ❆❧é♠ ❞✐ss♦✱bi,0 ≤bi,1 ≤bi,2✳
❆ ❋✐❣✉r❛ ✷✳✹ ✐❧✉str❛ ♦ ❣rá✜❝♦ ❞❛ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛❝✉♠✉❧❛❞❛ s♦❜ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ❝♦♠ ✸
❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛✳
❆ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❡ ✉♠ ✐♥❞✐✈✐❞✉♦✱ ❝♦♠ ✈❛❧♦r ❞❡ ♣r♦✜❝✐ê♥❝✐❛ θ✱ ❡s❝♦❧❤❡r ❛ ❝❛t❡❣♦r✐❛ ❦ ♥♦ ✐t❡♠i
é✿
Pi,k(θ) =Pi,k+(θ)−Pi,k++1(θ), ✭✷✳✷✮
✽ ▼❊❚❖❉❖▲❖●■❆ ❚❆■✲P■ ✷✳✷
❋✐❣✉r❛ ✷✳✹✿ ❊①❡♠♣❧♦ ❞❡ ✉♠❛ ❝✉r✈❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❛❝✉♠✉❧❛❞❛ s♦❜ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ❝♦♠ ✸ ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛✳
✷✳✹ ❊❙❚■▼❆➬➹❖ ❉❖ ❚❘❆➬❖ ▲❆❚❊◆❚❊ ✾
❙✉♣♦♥❞♦ l−1 ✐t❡♥s ❥á ❛❞♠✐♥✐str❛❞♦s✱ ❛ ❢✉♥çã♦ ❞❡ ✈❡r♦ss✐♠✐❧❤❛♥ç❛ ❞♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ é✿
L(θ|x) =
l−1 Y
i=1
f(xi|θ) =
l−1 Y
i=1 2 Y
k=0
Pxik
i,k (θ), ✭✷✳✸✮
❡♠ q✉❡Pi,k(θ) é ❞❛❞♦ ❡♠✷✳✷✱k= 0,1,2r❡♣r❡s❡♥t❛ ❛s ❝❛t❡❣♦r✐❛s ❞♦s ✐t❡♥s✱x= (x1, ...,xl−1),xi=
(xi0, xi1, xi2) ❡xik sã♦ ✈❛r✐á✈❡✐s q✉❡ ❛ss✉♠❡♠ ♦ ✈❛❧♦r ✶ s❡ ❛ ❝❛t❡❣♦r✐❛k❞♦ ✐t❡♠ i❢♦r ❡s❝♦❧❤✐❞❛ ❡ ✵✱
❝❛s♦ ❝♦♥trár✐♦✳
✷✳✸ ❊st✐♠❛çã♦ ❞♦ tr❛ç♦ ❧❛t❡♥t❡
❖ ♠ét♦❞♦ ❊❆P ❢♦✐ ✉s❛❞♦ ♣❛r❛ ❛ ❡st✐♠❛çã♦ ❞❡ θ✱ s❡❣✉✐♥❞♦ ♦ ❝♦♥❤❡❝✐❞♦ ❢❛t♦ ❞❛ ❡st✐♠❛çã♦ ❜❛②❡✲
s✐❛♥❛ ❢✉♥❝✐♦♥❛r ♠❡❧❤♦r ❡♠ ❚❆■✳ ❇❛❦❡r ✭✷✵✵✶✮✱ ❇❛❦❡r ✫ ❑✐♠ ✭✷✵✵✹✮✱ ▼✐s❧❡✈② ✫ ❙t♦❝❦✐♥❣ ✭✶✾✽✾✮
s✉❣❡r✐❛♠ q✉❡ ❛ ❡st✐♠❛t✐✈❛ ♣♦♥t✉❛❧ ❞❡ θ s❡❥❛ ♦❜t✐❞❛ ♣♦r ❊❆P ♣♦rq✉❡ ♦ ♠ét♦❞♦ ♣♦❞❡ s❡r ❝❛❧❝✉❧❛❞♦
s❡♠ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠ét♦❞♦s ✐t❡r❛t✐✈♦s✱ ♦ q✉❡ ❞✐♠✐♥✐✉ t❡♠♣♦ ❞❡ ❡st✐♠❛çã♦✳ ❆ ❞✐str✐❜✉✐çã♦✱ ❡s♣❡✲
r❛♥ç❛ ❡ ✈❛r✐â♥❝✐❛ ❛ ♣♦st❡r✐♦r✐ ❞❡θ✱ ❝♦♥❞✐❝✐♦♥❛❞❛s ❛♦s ❞❛❞♦s ♦❜s❡r✈❛❞♦s✱ sã♦ ❞❛❞❛s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱
♣❡❧❛s ❡①♣r❡ssõ❡s✷✳✹✱✷✳✺❡ ✷✳✻✳
π(θ)∝L(θ|x)g(θ|λ), ✭✷✳✹✮
E(θ|x, λ) = R
RθL(θ|x)g(θ|λ)dθ R
RL(θ|x)g(θ|λ)dθ
, ✭✷✳✺✮
V ar(θ|x, λ) = R
R(θ−E(θ)) 2
L(θ|x)g(θ|λ)dθ R
RL(θ|x)g(θ|λ)dθ
, ✭✷✳✻✮
❡♠ q✉❡ g(θ|λ) é ❛ ❞✐str✐❜✉✐çã♦ ❛ ♣r✐♦r✐ ❞❡θ ❡ λsã♦ ♦s ❤✐♣❡r♣❛râ♠❡tr♦s✳
❖ ♠ét♦❞♦ ♥✉♠ér✐❝♦ ❞❡ q✉❛❞r❛t✉r❛ ❣❛✉ss✐❛♥❛ ✭❉❡❤❣❤❛♥ ❡t ❛❧✳✱✷✵✵✻✮ ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ♦ ❝á❧❝✉❧♦
❞❛s ✐♥t❡❣r❛✐s✳
✷✳✹ ❙❡❧❡çã♦ ❞❡ ✐t❡♥s
P❛r❛ ❛ s❡❧❡çã♦ ❞♦s ✐t❡♥s ❛ ❝❛❞❛ ♣❛ss♦ ❞♦ ❚❆■✲P■✱ ♥ã♦ ❢♦✐ ❛❞♦t❛❞♦ ♦ ❝r✐tér✐♦ ♠❛✐s tr❛❞✐❝✐♦♥❛❧
❞❛ ❧✐t❡r❛t✉r❛ ✭✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r✮✳ ■st♦ ♣♦rq✉❡ s❡ ❛ ❡st✐♠❛t✐✈❛ ❝♦rr❡♥t❡ ❞❡ θ ❢♦r ❞✐st❛♥t❡ ❞♦ s❡✉
✈❛❧♦r r❡❛❧✱ ❡st❡ ❝r✐tér✐♦ ♣♦❞❡ s❡r ✐♥❛❞❡q✉❛❞♦✳ ◆✉♠ ❚❆■✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ♥♦s ♣❛ss♦s ✐♥✐❝✐❛✐s✱ é ♠✉✐t♦ ♣♦ssí✈❡❧ q✉❡ ✐ss♦ ♦❝♦rr❛✳
P❛r❛ ♦ i✲és✐♠♦ ✐t❡♠✱ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r ♣❛r❛ ✉♠ ✈❛❧♦r ❞❡ tr❛ç♦ ❧❛t❡♥t❡θ é ❞❡✜♥✐❞❛ ♣♦r✿
Ii(θ) =E "
∂
∂θlogf(Xi.|θ)
2#
✭✷✳✼✮
❝♦♠f(Xi.|θ) s❡♥❞♦ ❛ ❢✉♥çã♦ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞❡ ❞❛ r❡s♣♦st❛ ❞❛❞❛ ♣❡❧♦ ♠♦❞❡❧♦ ✷✳✷✱ ♦✉ s❡❥❛✱ ❡s♣❡❝✐✜✲
❝❛♠❡♥t❡ ♣❛r❛ ♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛✳ P♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ✷✳✼ é ❝❛❧❝✉❧❛❞❛ ❡♠ ❢✉♥çã♦ ❞❡θ✱ q✉❡ é
s✉❜st✐t✉✐❞♦ ♣❡❧❛ ❡st✐♠❛t✐✈❛ ❝♦rr❡♥t❡✳ ❙❡ ❡ss❛ ❡st✐♠❛t✐✈❛ ❡st✐✈❡r ♠✉✐t♦ ❞✐st❛♥t❡ ❞♦ ✈❡r❞❛❞❡✐r♦ ✈❛❧♦r✱ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❋✐s❤❡r s❡rá ♠❛①✐♠✐③❛❞❛ ❡♠ ✉♠ ♣♦♥t♦ ❞✐st❛♥t❡ ❞♦ r❡❛❧ ❡✱ ♣♦rt❛♥t♦✱ ♣♦❞❡ ❡st❛r ♠✉✐t♦ ❡q✉✐✈♦❝❛❞❛✳
❆ ✐♥❢♦r♠❛çã♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r✱ ❛ q✉❛❧ ♠❡❞❡ ❛ ❞✐stâ♥❝✐❛ ❡♥tr❡ ❞✉❛s ✈❡r♦ss✐♠✐❧❧❤❛♥ç❛s ♣❛r❛ ✉♠ ♠❡s♠♦ ❡s♣❛ç♦ ♣❛r❛♠étr✐❝♦✱ é q✉❡ ❢♦✐ ❡s❝♦❧❤✐❞❛ ♣❛r❛ ✐♠♣❧❡♠❡♥t❛çã♦ ♥♦ ❚❆■✲P■✱ ❝♦♥❢♦r♠❡ s✉❣❡r✐❞♦ ♣♦r ❈❤❛♥❣ ✫ ❨✐♥❣ ✭✶✾✾✻✮✳ ◗✉❛♥t♦ ♠❛✐♦r ♦ ✈❛❧♦r ❞❡ss❛ ✐♥❢♦r♠❛çã♦✱ ♠❛✐♦r ❛ ❞✐s❝r❡♣â♥❝✐❛ ❡♥tr❡ ❛s ❞✉❛s ❢✉♥çõ❡s✳ ❆ ♠❡❞✐❞❛ ❞❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ♣❛r❛ ♦ ✐✲és✐♠♦ ✐t❡♠ ♥♦ t❡st❡ ❡♥tr❡ ♦s
✶✵ ▼❊❚❖❉❖▲❖●■❆ ❚❆■✲P■ ✷✳✺
Ki(θ,bθ) = E "
logf(Xi|θ)
f(Xi|θb) # ✭✷✳✽✮ = 2 X k=0
Pi,k(θ) log
Pi,k(θ)
Pi,k(θb)
❱❛❧❡ ❧❡♠❜r❛r q✉❡✱ ❝♦♠♦ t❡♠♦s ✐♥❞❡♣❡♥❞ê♥❝✐❛ ❝♦♥❞✐❝✐♦♥❛❧ ❡♥tr❡ ❛s r❡s♣♦st❛s✱ ❛ ✐♥❢♦r♠❛çã♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ❛♣ós ❧✲✶ ✐t❡♥s ❛❞♠✐♥✐str❛❞♦s é ❡s❝r✐t❛ ❝♦♠♦✿
Kl−1(θ,θb) = l−1 X
i=1
Ki(θ,θb). ✭✷✳✾✮
❯♠❛ ✈❡③ q✉❡ ♦ ✈❡r❞❛❞❡✐r♦ ✈❛❧♦r ❞♦ tr❛ç♦ ❧❛t❡♥t❡ (θ) é ❞❡s❝♦♥❤❡❝✐❞♦✱ ❙❛♥❞s ❛♥❞ ❲❛t❡rs ✭✶✾✾✻✮
♣r♦♣✉s❡r❛♠ ❝♦♥s✐❞❡r❛r ✭✷✳✽✮ ❡♠ ✉♠ ✐♥t❡r✈❛❧♦ ❞❡ ❝♦♥✜❛♥ç❛ ❞♦ tr❛ç♦ ❧❛t❡♥t❡[θb−δl,θb+δl]✱ s❡♥❞♦δl
✉♠❛ ❢✉♥çã♦ ❞❡❝r❡s❝❡♥t❡ ❡♠ r❡❧❛çã♦ ❛ ❧ ✭♣❛ss♦ ❝♦rr❡♥t❡ ❞♦ ❚❆■✮✳ ❆ss✐♠ ♦ ❝r✐tér✐♦ ♣❛r❛ s❡❧❡❝✐♦♥❛r ♦ ♣ró①✐♠♦ ✐t❡♠ ❛ s❡r ❛♣r❡s❡♥t❛❞♦ ♥♦ t❡st❡ é ❞❛❞♦ ♣♦r✿
il ≡argmax i
(Z θb+δl
b
θ−δl
Ki(θ,θb)dθ:iǫL )
✭✷✳✶✵✮
s❡♥❞♦δl=zγ/
√
l ❡ ▲✱ ♦ ❝♦♥❥✉♥t♦ ❞♦s ✐t❡♥s ❛✐♥❞❛ ♥ã♦ ❛♣r❡s❡♥t❛❞♦s ❛♦ ✐♥❞✐✈í❞✉♦ ♥♦ t❡st❡✳
✷✳✺ ❙❤❛❞♦✇ t❡st
❖ ❝r✐tér✐♦ ❞❡ s❡❧❡çã♦ ❡①♣r❡ss♦ ❡♠ ✭✷✳✶✵✮ ♥ã♦ ❧❡✈❛ ❡♠ ❝♦♥s✐❞❡r❛çã♦ ♥❡♥❤✉♠❛ r❡str✐çã♦ s✉❜❥❡t✐✈❛
♣❛r❛ ❛ ❝♦♠♣♦s✐çã♦ ❞♦ t❡st❡✳ P♦r ❡①❡♠♣❧♦✱ ✉♠❛ ❛✈❛❧✐❛çã♦ ❛❞❡q✉❛❞❛ ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❡♠ ✐♥❣❧ês ❞❡✈❡ ❝♦♥t❡♠♣❧❛r ✐t❡♥s ❛ss♦❝✐❛❞♦s ❛ ❝❛❞❛ ✉♠ ❞♦s três ♠♦❞✉❧♦s✿ ❡str✉t✉r❛ ❞❡ t❡①t♦ ❝✐❡♥tí✜❝♦✱ ❝♦♠♣r❡❡♥sã♦ ❞❡ t❡①t♦ ❡ ❝♦♥✈❡♥çõ❡s ❣r❛♠❛t✐❝❛✐s ❞❛ ❧í♥❣✉❛✳ ❆ ♥ã♦ ✐♠♣♦s✐çã♦ ❞❡ss❛ r❡str✐çã♦ ♣♦❞❡ ❣❡r❛r t❡st❡s ❝♦♠ ♥❡♥❤✉♠ ✐t❡♠ ❞❡ ✉♠ ❞♦s ♠ó❞✉❧♦s ❡ ✉♠ ♥ú♠❡r♦ ❡①❝❡ss✐✈♦ ❞❡ ✐t❡♥s ❞❡ ♦✉tr♦✱ ❞✐st♦r❝❡♥❞♦ ❛ ❛✈❛❧✐❛çã♦ ❞❡s❡❥❛❞❛✳ ❖✉tr❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♦r❞❡♠ ♣rát✐❝❛ ❞✐③ r❡s♣❡✐t♦ ❛♦ ♥ú♠❡r♦ ❞❡ ✐t❡♥s ❡ ❞❡ t❡①t♦s ♥♦ t❡st❡✳ ❉♦✐s ✐♥❞✐✈í❞✉♦s q✉❡ r❡❛❧✐③❛♠ t❡st❡s ❝♦♠ ♥ú♠❡r♦s ✭❡ t❛♠❛♥❤♦s✮ ❞❡ t❡①t♦s ♠✉✐t♦ ❞✐st♦❛♥t❡s ♦✉ ❝♦♠ ♥ú♠❡r♦s ❞❡ ✐t❡♥s ♠✉✐t♦ ❞✐❢❡r❡♥t❡s ♣♦❞❡♠ ❣❡r❛r ❛ s❡♥s❛çã♦ ❞❡ ✐♥❥✉st✐ç❛ ♥❛ ❝♦♠♣❛r❛çã♦ ❞❛s ❡st✐♠❛t✐✈❛s ❞❛s r❡s♣❡❝t✐✈❛s ♣r♦✜❝✐ê♥❝✐❛s✳ ❖ ✐♥❞✐✈í❞✉♦ q✉❡ r❡s♣♦♥❞❡✉ ✉♠ t❡st❡ ❝♦♠ ♠✉✐t♦s t❡①t♦s ♦✉ ♠✉✐t♦ ❧♦♥❣♦ ♣♦❞❡ r❡❝❧❛♠❛r q✉❡ ♦ ❝❛♥s❛ç♦ ❢♦✐ ♠❛✐♦r ❡✱ ♣♦rt❛♥t♦✱ ♦ ❞❡s❣❛st❡ ❛♦ ❧♦♥❣♦ ❞❛ r❡❛❧✐③❛çã♦ ❞❛ ♣r♦✈❛ ♣♦❞❡ t❡r ✐♥✢✉❡♥❝✐❛❞♦ ❞❡ ❢♦r♠❛ ♥ã♦ ❡q✉✐♣❛rá✈❡❧ ❡♥tr❡ ♦s ✐♥❞✐✈í❞✉♦s✳ P♦r ♦✉tr♦ ❧❛❞♦✱ ❛q✉❡❧❡ q✉❡ r❡s♣♦♥❞❡✉ ✉♠ t❡st❡ ❝✉rt♦✱ ❝♦♠ ♣♦✉❝♦s ✐t❡♥s✱ ♣♦❞❡ r❡❝❧❛♠❛r q✉❡ ♥ã♦ ❤♦✉✈❡ ✏t❡♠♣♦✧✭✐✳❡✳✱ ♥ú♠❡r♦ ❞❡ ✐t❡♥s✮ s✉✜❝✐❡♥t❡ ♣❛r❛ q✉❡ s✉❛ r❡❛❧ ♣r♦✜❝✐ê♥❝✐❛ s❡❥❛ ❡✈✐❞❡♥❝✐❛❞❛✳
❯♠❛ ❞❛s ♣r♦♣♦st❛s ♠❛✐s ✐♥t❡r❡ss❛♥t❡s ♥❛ ❧✐t❡r❛t✉r❛ ♣❛r❛ ✉♠❛ ❢á❝✐❧ ✐♥❝❧✉sã♦ ❞❡ r❡str✐çõ❡s ❞❡ss❡
t✐♣♦ é ❛ ❛❜♦r❞❛❣❡♠ ❙❤❛❞♦✇ t❡st ✭❱❛♥ ❞❡r ▲✐♥❞❡♥✱ ✷✵✵✵✮✳ ❖ ♠ét♦❞♦ ❞❡ ♦t✐♠✐③❛çã♦ ❞❡ ♣r♦❣r❛♠❛çã♦
❧✐♥❡❛r ✐♥t❡✐r❛ é ✉s❛❞♦ ♣❛r❛ ♦❜t❡♥çã♦ ❞❡ ✉♠ s✉❜❝♦♥❥✉♥t♦ ✭❞❡ t❛♠❛♥❤♦n✱ ♣r❡✈✐❛♠❡♥t❡ ✜①❛❞♦✮ ❞❡ ✐t❡♥s
❞♦ ❜❛♥❝♦ q✉❡ ♠❛①✐♠✐③❛ ❛ ✐♥❢♦r♠❛çã♦ ✭✷✳✾✮✱ t♦♠❛♥❞♦ l−1 =n✱ s✉❥❡✐t❛ às r❡str✐çõ❡s ❞❡ ✐♥t❡r❡ss❡✱
t❛♠❜é♠ ♣r❡✈✐❛♠❡♥t❡ ❞❡✜♥✐❞❛s✳ ❯♠ ❝♦♥❥✉♥t♦ ❞❡ n ✐t❡♥s é ♦❜t✐❞♦ ❡♠ ❝❛❞❛ ♣❛ss♦ ❞♦ ❛❧❣♦rít♠♦✱
❣❡r❛♥❞♦ ✉♠ t❡st❡ ❝♦♠♦ ❝♦♥❥✉♥t♦ s♦❧✉çã♦✳ ➱ ✐♠♣♦rt❛♥t❡ ❞❡st❛❝❛r q✉❡ ✉♠❛ ❞❛s r❡str✐çõ❡s ❞♦ t❡st❡
♥♦ ♣❛ss♦ l é q✉❡ t♦❞♦s ♦s ✐t❡♥s ❥á ❛❞♠✐♥✐str❛❞♦s ❛♥t❡r✐♦r♠❡♥t❡ ❡stã♦ ♣r❡s❡♥t❡s ♥♦ t❡st❡ ❝♦rr❡♥t❡✳
❖ ✐t❡♠ ❛ s❡r ❛❞♠✐♥✐str❛❞♦ ♥♦ ♣❛ss♦ l ❞♦ t❡st❡ é ❛q✉❡❧❡ ♥ã♦ ❛♣r❡s❡♥t❛❞♦ ♥♦s ♣❛ss♦s ❛♥t❡r✐♦r❡s✱ q✉❡
♣❡rt❡♥ç❛ ❛♦ ❝♦♥❥✉♥t♦ s♦❧✉çã♦ ❞♦ ♣❛ss♦ ❝♦rr❡♥t❡ ❡ q✉❡ ❛♣r❡s❡♥t❡ ❛ ♠á①✐♠❛ ✐♥❢♦r♠❛çã♦ ✭✷✳✽✮ ♣❛r❛ ♦
❛t✉❛❧ ✈❛❧♦r ❡st✐♠❛❞♦θˆ✳ ❉❡♣♦✐s ❞♦ ✐t❡♠ s❡r ❛❞♠✐♥✐str❛❞♦✱ ♦ r❡st❛♥t❡ ❞♦s ✐t❡♥s ♥ã♦ ✉t✐❧✐③❛❞♦s ♥♦ t❡st❡
✈♦❧t❛♠ ♣❛r❛ ♦ ❜❛♥❝♦ ❞❡ ✐t❡♥s ❝♦♠♦ ✐t❡♥s ❞✐s♣♦♥í✈❡✐s ❛ s❡r❡♠ ❛❞♠✐♥✐str❛❞♦s ♥❛s ♣ró①✐♠❛s s❡❧❡çõ❡s ❞♦ ❙❤❛❞♦✇ t❡st✳ ❯♠❛ r❡♣r❡s❡♥t❛çã♦ ❜❛st❛♥t❡ ✐❧✉str❛t✐✈❛ ❞♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞♦ ❙❤❛❞♦✇ t❡st ❡♥❝♦♥tr❛✲s❡
✷✳✻ ❈❘■❚➱❘■❖ ❉❊ ■◆❮❈■❖ ❊ P❆❘❆❉❆ ✶✶
❋✐❣✉r❛ ✷✳✻✿ ❘❡♣r❡s❡♥t❛ç❛♦ ❞♦ ❙❤❛❞♦✇ t❡st✳ ❋♦♥t❡✿ ✈❛♥ ❞❡r ▲✐♥❞❡♥✱ ✷✵✶✵✳
❯♠ ❡s♣❡❝✐❛❧ ❝✉✐❞❛❞♦ ❞❡✈❡ s❡r t♦♠❛❞♦ ♥❛ ♣r❡s❡♥ç❛ ❞❡ ✐t❡♥s ❛ss♦❝✐❛❞♦s ❛ ✉♠ ♠❡s♠♦ t❡①t♦ ♦✉ ✜❣✉r❛ ✭❣❡♥❡r✐❝❛♠❡♥t❡ ❞❡♥♦♠✐♥❛❞♦ ✏❡stí♠✉❧♦✧✮✳ ❊♠ s✐t✉❛çõ❡s r❡❛✐s✱ ♦ ✐❞❡❛❧ é ❛♣r❡s❡♥t❛r t♦❞♦s ♦s ✐t❡♥s ❛ss♦✲
❝✐❛❞♦s ❛♦ ♠❡s♠♦ ❡stí♠✉❧♦ s❡q✉❡♥❝✐❛❧♠❡♥t❡ ✭❱❛♥ ❞❡r ▲✐♥❞❡♥ ✫ ●❧❛s✱✷✵✶✵❀❱❛♥ ❞❡r ▲✐♥❞❡♥ ✫ P❛s❤❧❡②
✱✷✵✶✵✮✳ ◆❡st❡ tr❛❜❛❧❤♦✱ q✉❛♥❞♦ ✉♠ ❡stí♠✉❧♦ ♥♦✈♦ ❛♣❛r❡❝❡ ❡♠ ✉♠❛ ❝❡rt❛ ✐t❡r❛çã♦ ❞♦ ❙❤❛❞♦✇ t❡st✱
t♦❞♦s ♦s ✐t❡♥s ❛ss♦❝✐❛❞♦s àq✉❡❧❡ ❡stí♠✉❧♦ ♥♦ ❙❤❛❞♦✇ t❡st ❞❡ss❛ ✐t❡r❛çã♦ ✐rã♦ s❡r ❛♣r❡s❡♥t❛❞♦s ❝♦♥✲ s❡❝✉t✐✈❛♠❡♥t❡ ❛♦ ✐♥❞✐✈í❞✉♦✳
✷✳✻ ❈r✐tér✐♦ ❞❡ ✐♥í❝✐♦ ❡ ♣❛r❛❞❛
❖ ♥í✈❡❧ ❞❡ ❝♦♥❤❡❝✐♠❡♥t♦ ✐♥✐❝✐❛❧ é ❛ ❡st✐♠❛t✐✈❛ ✐♥✐❝✐❛❧ ♣r♦✈✐sór✐❛ ❞❛ ♣r♦✜❝✐ê♥❝✐❛✱ ♥❡❝❡ssár✐❛ ♣❛r❛
♦ ✐♥í❝✐♦ ❞♦ t❡st❡ ❡ r❡❧❛❝✐♦♥❛❞❛ ❝♦♠ ♦ ♥í✈❡❧ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ❞❛ ♣r✐♠❡✐r❛ q✉❡stã♦✳❈♦♥❡❥♦ ❡t ❛❧✳ ✭✷✵✵✶✮
❝♦♥s✐❞❡r❛ q✉❡ ♦ ♥í✈❡❧ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ❞❛ ♣r✐♠❡✐r❛ q✉❡stã♦ ❞❡✈❡ s❡r ❡s❝♦❧❤✐❞♦ ❞❡ ❢♦r♠❛ ❛ ♣♦ss✐❜✐❧✐t❛r
✉♠❛ r❡❞✉çã♦ ♥♦ t❡♠♣♦ ❞❡ t❡st❡✳ ❙✉❦❛♠♦❧s♦♥ ✭✷✵✵✷✮ s❛❧✐❡♥t❛ q✉❡ ✉s✉❛❧♠❡♥t❡ ❛ ♣r✐♠❡✐r❛ q✉❡stã♦
♣♦ss✉✐ ✉♠ ♥í✈❡❧ ❞❡ ❞✐✜❝✉❧❞❛❞❡ ♠é❞✐♦✳ ❈♦♠♦ ❛ ♣r✐♥❝í♣✐♦ ♥ã♦ s❡ s❛❜❡ q✉❛❧ ❛ ❤❛❜✐❧✐❞❛❞❡ ❞♦ r❡s♣♦♥❞❡♥t❡✱ ✉♠ ✐t❡♠ ♠é❞✐♦ é ❛ ♠❡❧❤♦r ♦♣çã♦ ✐♥✐❝✐❛❧✳
❈♦♠♦ ♥❡♥❤✉♠❛ ✐♥❢♦r♠❛çã♦ ♣ré✈✐❛ ❞❛ ♣r♦✜❝✐ê♥❝✐❛ ❞♦s ❛❧✉♥♦s é ❝♦♥❤❡❝✐❞❛ ❞❡❝✐❞✐✉✲s❡ ✐♥✐❝✐❛r ❝♦♠
✉♠ ✈❛❧♦r ♠é❞✐♦θb0 = 0♣❛r❛ t♦❞♦s✳
❈❛♣ít✉❧♦ ✸
❊st✉❞♦ ❞❡ s✐♠✉❧❛çã♦
❊st❡ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦ ❢♦✐ ❡①❡❝✉t❛❞♦ ❡♠ s♦❢t✇❛r❡ ❘ ❡ ❞❡❧✐♥❡❛❞♦ ♣❛r❛ ✐❧✉str❛r ♦ ❢✉♥❝✐♦♥❛♠❡♥t♦ ❞❡ ✉♠ ❚❆■✱ ❡♠ t❡r♠♦s ❞❛ ❡✜❝✐ê♥❝✐❛ ♥❛ ❡st✐♠❛çã♦ ❞♦ tr❛ç♦ ❧❛t❡♥t❡✱ ❝♦♠♣❛r❛♥❞♦ ❞✐str✐❜✉✐çõ❡s ❛ ♣r✐♦r✐s ♥❛ ✉t✐❧✐③❛çã♦ ❞♦ ❊❆P ❡ ♥ú♠❡r♦s ❞✐❢❡r❡♥t❡s ❞❡ ✐t❡♥s ♥♦ t❡st❡ ✭✶✵✱ ✷✵✱ ✷✺ ❡ ✸✵✮✳ P❛r❛ ♦ ❜❛♥❝♦
❞❡ ✐t❡♥s ❢♦r❛♠ s✐♠✉❧❛❞♦s ✺✵✵ ✐t❡♥s ❝♦♠ ✸ ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛s✱ ❝♦♠ a ∼ lognormal(0.7,0.1)✱
❣❡r❛♥❞♦ ❛♣❡♥❛s ❜♦♥s ✈❛❧♦r❡s ♣❛r❛ ♦s ♣❛râ♠❡tr♦s ❞❡ ❞✐✜❝✉❧❞❛❞❡ ✭▼✐s❧❡✈②✱ ✶✾✽✻✮✱ ❡ bi ∼ N(0,1.2)
❝♦♠ b1 < b2✱ ❝♦♠ ❜❛s❡ ♥♦ ♠♦❞❡❧♦ ❞❡ ❙❛♠❡❥✐♠❛ ❝♦♠ ✸ ❝❛t❡❣♦r✐❛s ❞❡ r❡s♣♦st❛✳ ❖ ♠ét♦❞♦ ❊❆P ❢♦✐ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❡st✐♠❛r ♦ tr❛ç♦ ❧❛t❡♥t❡ ❞♦ ♠❡s♠♦ ♠♦❞❡❧♦ ❡ ♦ ❝r✐tér✐♦ ❞❡ ❑✉❧❧❜❛❝❦✲▲❡✐❜❧❡r ♣❛r❛ ❛
s❡❧❡çã♦ ❞❡ ✐t❡♥s✳ ❈♦♠♦ ❝r✐tér✐♦ ❞❡ ✐♥í❝✐♦ ❞♦ ❚❆■ ❢♦✐ ❛❞♦t❛❞♦ q✉❡ t♦❞♦s ❝♦♠ θˆ0 = 0 ❡ ❝♦♠♦ ❝r✐tér✐♦
❞❡ ♣❛r❛❞❛ ♥ú♠❡r♦ ❞❡ ✐t❡♥s ✜①♦s✭✶✵✱ ✷✵✱ ✷✺ ❡ ✸✵ ✐t❡♥s✮✳
◆♦ ♣r✐♠❡✐r♦ ❡st✉❞♦ ❞❡ s✐♠✉❧❛çã♦✱ ♣❛r❛ ❝❛❞❛ θ ∈ {−3,−2,−1,0,1,2,3} ❢♦r❛♠ s✐♠✉❧❛❞♦s ✷✵✵
t❡st❡s✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡ ♣❛r❛ ❝❛❞❛ t❡st❡ s✐♠✉❧❛❞♦✱ três t✐♣♦s ❞❡ ❞✐str✐❜✉✐çõ❡s ❛ ♣r✐♦r✐ ♣❛r❛ ❛s ❤❛✲ ❜✐❧✐❞❛❞❡s ❢♦r❛♠ ❛❞♦t❛❞❛s ♣❛r❛ ♦ ♠ét♦❞♦ ❊❆P✿ ◆✭✵✱✶✮✱ q✉❡ é ✉s✉❛❧♠❡♥t❡ ❛❞♦t❛❞❛ ♥❛ ❧✐t❡r❛t✉r❛✱
◆✭✵✱✷✮✱ ♣❛r❛ ❞❛r ♠❡♥♦s ✐♥❢♦r♠❛çã♦ s♦❜r❡ ♦ ♣❛râ♠❡tr♦ ❡♠ q✉❡stã♦ ❡N(ˆθi−1, σ
2(ˆθ
i−1))♣❛r❛ ❛♣r♦✈❡✐✲
t❛r ❛ ❡st✐♠❛t✐✈❛ ❝♦rr❡♥t❡ ❝♦♠♦ ✐♥❢♦r♠❛çã♦ ❛ ♣r✐♦r✐ ❞❛ ❤❛❜✐❧✐❞❛❞❡ ❞♦ ✐♥❞✐✈í❞✉♦✳ ❚♦t❛❧✐③❛♥❞♦ ❛ss✐♠ 7×3×200 = 4200 t❡st❡s s✐♠✉❧❛❞♦s✳
P❛r❛ ❛✈❛❧✐❛r ❛ q✉❛❧✐❞❛❞❡ ❞♦ ♠♦❞❡❧♦✱ ❢♦r❛♠ ❝❛❧❝✉❧❛❞❛s ❛s ♠❡❞✐❞❛s ❛ s❡❣✉✐r✿
V icio=
200 X
j=1
ˆ
θjl−θl
200 ,
EQM =
P200
j=1(ˆθjl−θl)2
200 ,
❡♠ q✉❡ j = 1, ...,200 r❡♣r❡s❡♥t❛ ❛s r❡♣❡t✐çõ❡s ❞❡ ❝❛❞❛ ✈❛❧♦r ✜①❛❞♦ ❞❡ θ✱ l = 1, ...,7 ✐♥❞❡①❛ ♦s ✼
✈❛❧♦r❡s ✜①❛❞♦s ♣❛r❛θ✱θl∈ {−3,−1,−2,0,1,2,3}sã♦ ♦s ✈❛❧♦r❡s ✜①❛❞♦s ♣❛r❛θ✱θˆjlé ❛ ❡st✐♠❛t✐✈❛ ❞❡
θl♦❜t✐❞❛ ♣❡❧♦ ♠ét♦❞♦ ❊❆P ♥❛ s✐♠✉❧❛çã♦✳ ❖s ✈❛❧♦r❡s ❡♥❝♦♥tr❛❞♦s sã♦ ❛♣r❡s❡♥t❛❞♦s ♥❛s ❚❛❜❡❧❛s✸✳✶
❡ ✸✳✷✱ ♥❛s q✉❛✐s ♣♦❞❡✲s❡ ♦❜s❡r✈❛r q✉❡ ♦ ✈í❝✐♦ s❡ ❛♣r♦①✐♠❛ ❞❡ ③❡r♦ ❡ ♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦
❞✐♠✐♥✉✐ ❝♦♥❢♦r♠❡ ❛✉♠❡♥t❛ ♦ ♥ú♠❡r♦ ❞❡ ✐t❡♥s ❡ q✉❡ ♦ ❣❛♥❤♦ ❡♠ ♣r❡❝✐sã♦ ❞❡ ❡st✐♠❛çã♦ ❛✉♠❡♥t❛♥❞♦ ♦ t❛♠❛♥❤♦ ❞♦ t❡st❡ ❞❡ ✷✺ ❡ ✸✵ t❛❧✈❡③ ♥ã♦ s❡❥❛ ✐♠♣♦rt❛♥t❡ ❡ ✷✵ ✐t❡♥s ❥á sã♦ s✉✜❝✐❡♥t❡s ❡♠ ✉♠ t❡st❡✳
❈♦♠ ❡①❝❡çã♦ ❞❛ ♣r✐♦r✐ N(ˆθi−1, σ
2
(ˆθi−1))✱ ❛s ❡st✐♠❛t✐✈❛s ❢♦r❛♠ ♠✉✐t♦ ♣ró①✐♠❛s ❞♦s ✈❛❧♦r❡s r❡❛✐s
♣❛r❛ ❛s ❞❡♠❛✐s ♣r✐♦r✐s ❛♣r❡s❡♥t❛❞❛s✱ ♦ q✉❡ ♣♦❞❡ s❡r ❝♦♥✜r♠❛❞♦ ♣❡❧♦s ❜❛✐①♦s ✈❛❧♦r❡s ❞♦ ✈í❝✐♦ ❡ ❞♦ ❡rr♦ q✉❛❞rát✐❝♦ ♠é❞✐♦✳ ◆♦ ❡♥t❛♥❞♦ ❛✉♠❡♥t❛♠ ❝♦♥s✐❞❡r❛✈❡❧♠❡♥t❡ q✉❛♥❞♦ s❡ é ✉s❛❞♦ ◆✭✵✱✶✮ ❝♦♠♦ ♣r✐♦r✐ ♣❛r❛ ✈❛❧♦r❡s ❞❡ ❤❛❜✐❧✐❞❛❞❡s ♠✉✐t♦ ❞✐st❛♥t❡s ❞❛ ♠é❞✐❛ ✭♦✉ s❡❥❛✱ ♣ró①✐♠♦s ❛ ✲✸✱✸✮✳
