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Some asymptotic results on density estimators by wavelet projections

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  • Varron, Davit

Abstract

Let (Xi)i>=1 be an i.i.d. sample on having density f. Given a real function [phi] on with finite variation, and given an integer valued sequence (jn), let denote the estimator of f by wavelet projection based on [phi] and with multiresolution level equal to jn. We provide exact rates of almost certain convergence to 0 of the quantity , when n2-djn/logn-->[infinity] and H is a given hypercube of . We then show that, if n2-djn/logn-->c for a constant c>0, then the quantity almost surely fails to converge to 0.

Suggested Citation

  • Varron, Davit, 2008. "Some asymptotic results on density estimators by wavelet projections," Statistics & Probability Letters, Elsevier, vol. 78(15), pages 2517-2521, October.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:15:p:2517-2521
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    References listed on IDEAS

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    1. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    2. Deheuvels, Paul, 1992. "Functional laws of the iterated logarithm for large increments of empirical and quantile processes," Stochastic Processes and their Applications, Elsevier, vol. 43(1), pages 133-163, November.
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