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Activity Number:
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382
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Type:
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Contributed
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Date/Time:
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Wednesday, August 1, 2007 : 8:30 AM to 10:20 AM
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Sponsor:
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Section on Nonparametric Statistics
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| Abstract - #309130 |
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Title:
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Adaptive Density Estimation Under Dependence
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Author(s):
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Olivier Wintenberger*+ and Irene Gannaz
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Companies:
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SAMOS and University Joseph Fourier
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Address:
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Centre Pierre Mends France, Paris Cedex 13, 75634, France
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Keywords:
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Adaptive estimation ; Asymptotic minimax ; Hard thresholding ; Wavelets ; Weak dependence ; Nonparametric density estimation
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Abstract:
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Assume that $(X_t)_{t\in\Z}$ is a real valued time series admitting a common marginal density $f$ with respect to Lebesgue measure. Donoho {\it et al.}~(1996) propose a near-minimax method based on thresholding wavelets to estimate $f$ on a compact set in an independent and identically distributed setting. The aim of the present work is to extend this methodology to different weakly dependent cases. Bernstein's type inequalities are proved to be sufficient to extend near-minimax results. Assumptions are detailed for dynamical systems and under the $\eta$-weak dependence condition from Doukhan & Louhichi (1999). The threshold levels in our estimator integrates the dependence structure of the sequence $(X_t)_{t\in\Z}$ through one parameter $\gamma$. The near minimaxity is obtained for $\L^p$-convergence rates ($p\ge 1$). An estimator of $\gamma$ is obtained by cross-validation procedure.
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