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Han-Ying Liang, Volker Mammitzsch, Josef Steinebach

Nonlinear wavelet density and hazard rate estimation for censored data under dependent observations

Keywords: nonlinear wavelet estimator, right censoring, density estimator, hazard rate estimator, alpha-mixing sequence

In this paper, we discuss the global L₂ error of the nonlinear wavelet estimators of the density function in the Besov space B_pq^s, when the survival times form a stationary α-mixing sequence, and prove that the nonlinear wavelet estimators can achieve the optimal rate of convergence, which is similar to the result of Donoho et al. (1996). Also, the optimal convergence rates of the nonlinear wavelet estimators of the hazard rate function in the Besov space B_pq^s are considered, which had not been discussed by Donoho et al. (1996) for complete data in the i.i.d. case.

Statistics & Decisions, Oldenbourg Wissenschaftsverlag

Print ISSN: 0721-2631
Volume: 23, 03/2005
Pages: 161 - 180

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