Facultade de Fisioterapia

Wavelet estimation of density for censored data with censoring indicator missing at random

Zou, Yu-Ye; Liang, Han-Ying
Abstract:
In this paper, we define the nonlinear wavelet estimator of density for the right censoring model with the censoring indicator missing at random (MAR), and develop its asymptotic expression for mean integrated squared error (MISE). Unlike for kernel estimator, the MISE expression of the estimator is not affected by the presence of discontinuities in the curve. Meanwhile, asymptotic normality of the estimator is established. The proposed estimator can reduce to the estimator defined by Li [Non-linear wavelet-based density estimators under random censorship. J Statist Plann Inference. 2003;117(1):35-58] when the censoring indicator MAR does not occur and a bandwidth in non-parametric estimation is close to zero. Also, we define another two nonlinear wavelet estimators of the density. A simulation is done to show the performance of the three proposed estimators.
Year:
2017
Type of Publication:
Article
Keywords:
Asymptotic normality; mean integrated squared error; missing at random; nonlinear wavelet estimator; right censorship
Journal:
Statistics
Volume:
51
Number:
6
Pages:
1214-1237
DOI:
10.1080/02331888.2017.1336170
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