Nonlinear wavelet density estimation with censored dependent data |
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Authors: | Si‐Li Niu |
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Affiliation: | Department of Mathematics, Tongji University, , Shanghai, 200092 China |
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Abstract: | In this paper, we provide an asymptotic expansion for the mean integrated squared error (MISE) of nonlinear wavelet estimator of survival density for a censorship model when the data exhibit some kind of dependence. It is assumed that the observations form a stationary and α‐mixing sequence. This asymptotic MISE expansion, when the density is only piecewise smooth, is same. However, for the kernel estimators, the MISE expansion fails if the additional smoothness assumption is absent. Also, we establish the asymptotic normality of the nonlinear wavelet estimator. Copyright © 2011 John Wiley & Sons, Ltd. |
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Keywords: | nonlinear wavelet density estimator censored data α ‐mixing mean integrated squared error asymptotic normality |
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