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Global L₂ error of wavelet density estimator with truncated and strong mixing observations

Yu-Ye Zou

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

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and

Han-Ying Liang

Department of Mathematics, Tongji University, Shanghai 200092, P. R. China

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https://doi.org/10.1142/S0219691314500337Cited by:2 (Source: Crossref)

Abstract

In this paper, we discuss the global L₂-error of the nonlinear wavelet estimator of density in the Besov space for the truncation model when the data exhibit strong mixing assumption, and prove that the estimator can achieve the optimal rate of convergence, which is similar to that in the complete and independent data case with term-by-term thresholding of the empirical wavelet coefficients (D. L. Donoho, I. M. Johnstone, G. Kerkyacharian and D. Picard, Density estimation by wavelet thresholding, Ann. Statist.24 (1996) 508–539). In addition, the conclusion shows that the convergence rate of the nonlinear estimator is faster than that of its linear estimator in some range.

Keywords:

AMSC: 62G07, 62G20

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