Wavelet estimation of density for censored data with censoring indicator missing at random. Issue 6 (2nd November 2017)

• Record Type: Journal Article
• Authors: Zou, Yu-Ye; Liang, Han-Ying
• Is Part Of: Statistics. Volume 51:Issue 6(2017)
• Page Start: 1214
• Page End: 1237
• Publication Date: 2017-11-02
• Subjects: Asymptotic normality -- mean integrated squared error -- missing at random -- nonlinear wavelet estimator -- right censorship; 62G07 -- 62G20; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2017.1336170
• Languages: English
• ISSNs: 0233-1888

Abstract

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.