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On the integrated squared error of the linear wavelet density estimator. (English) Zbl 1432.62088

Summary: The object of this paper is to study some asymptotic properties of the integrated squared error of a linear wavelet density estimator, \(\|\hat f_n-f\|_{L_2(\mathbb R)}^2\). We provide the exact almost sure rate of concentration about its mean, in fact a law of the iterated logarithm. Regarding the rate in probability, we obtain a polynomial upper bound for the rate of convergence in the central limit theorem of S. Zhang and Z. Zheng [Commun. Stat., Theory Methods 28, No. 5, 1093–1104 (1999; Zbl 0920.62063)].

MSC:

62G07 Density estimation
62G20 Asymptotic properties of nonparametric inference
60F05 Central limit and other weak theorems

Citations:

Zbl 0920.62063
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References:

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