Some asymptotic results on density estimators by wavelet projections

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• 作者：Davit Varron
• 刊名：Statistics and Probability Letters
• 出版年：2008
• 出版时间：15 October 2008
• 年：2008
• 卷：78
• 期：15
• 页码：2517-2521
• 全文大小：288 K

文摘

Let (X_i)_i≥1 be an i.i.d. sample on having density f. Given a real function on with finite variation, and given an integer valued sequence (j_n), let denote the estimator of f by wavelet projection based on and with multiresolution level equal to j_n. We provide exact rates of almost certain convergence to 0 of the quantity , when n2^−dj_n/logn→∞ and H is a given hypercube of . We then show that, if n2^−dj_n/logn→c for a constant c>0, then the quantity almost surely fails to converge to 0.