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[PENDING] Contributions of Wavelet Leaders and Bootstrap to Multifractal Analysis: Images, Estimation Performance, Dependence Structure and Vanishing Moments. Confidence Intervals and Hypothesis Tests.

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Figure 2.1: Von Koch curve. Iterative construction principle of the von Koch curve (left), and the curve after n = 6 iterations
Figure 2.2: Trajectories and increments of H-sssi processes. Trajectories (left), quantile-quantile plots versus standard normal (quantiles given by abscissa) of normal-ized empirical distributions of increments (center), and normalnormal-ized empirical d
Figure 2.4: Definition of Wavelet Leaders: 2d. The wavelet Leader L X (j, k 1 , k 2 ) at scale 2 j and position (k 1 , k 2 ) (black cross) is defined as the largest of the wavelet co-efficients | d (m) X (j ′ , k 1′ , k ′ 2 ) | , m = 1, · · · , 3 (’ • ’,
Figure 2.5: Analysis of cusp-type and oscillating singularities. Analysis of cusp-type (left) and chirp-type (right) singularities (top row) with wavelet coefficients (center row) and Leaders (bottom row): Whereas wavelet Leaders reproduce the H ¨older exp
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