Wavelet based estimation for the derivative of a density by block thresholding under random censorship

Esmaeil Shirazi; Yogendra P. Chaubey; Hassan Doosti; Hossein Ali Nirumand

doi:10.1016/j.jkss.2011.08.004

Wavelet based estimation for the derivative of a density by block thresholding under random censorship

Esmaeil Shirazi^*, Yogendra P. Chaubey, Hassan Doosti, Hossein Ali Nirumand

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003, 2008). We find bounds for the L ₂-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil (1995), Prakasa Rao (1996) and Li (2003, 2008) are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.

Original language	English
Pages (from-to)	199-211
Number of pages	13
Journal	Journal of the Korean Statistical Society
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/j.jkss.2011.08.004
Publication status	Published - Jun 2012
Externally published	Yes

Keywords

Adaptive estimation
Block thresholding
Censored data
Nonparametric estimator of derivative of a density
Primary
Rates of convergence
Secondary

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title = "Wavelet based estimation for the derivative of a density by block thresholding under random censorship",

abstract = "We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003, 2008). We find bounds for the L 2-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil (1995), Prakasa Rao (1996) and Li (2003, 2008) are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.",

keywords = "Adaptive estimation, Block thresholding, Censored data, Nonparametric estimator of derivative of a density, Primary, Rates of convergence, Secondary",

author = "Esmaeil Shirazi and Chaubey, {Yogendra P.} and Hassan Doosti and Nirumand, {Hossein Ali}",

year = "2012",

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T1 - Wavelet based estimation for the derivative of a density by block thresholding under random censorship

AU - Shirazi, Esmaeil

AU - Chaubey, Yogendra P.

AU - Doosti, Hassan

AU - Nirumand, Hossein Ali

PY - 2012/6

Y1 - 2012/6

N2 - We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003, 2008). We find bounds for the L 2-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil (1995), Prakasa Rao (1996) and Li (2003, 2008) are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.

AB - We consider wavelet based method for estimating derivatives of a density via block thresholding when the data obtained are randomly right censored. The proposed method is analogous to that of Hall and Patil (1995) for density estimation in the complete data case that has been extended recently by Li (2003, 2008). We find bounds for the L 2-loss over a large range of Besov function classes for the resulting estimators. The results of Hall and Patil (1995), Prakasa Rao (1996) and Li (2003, 2008) are obtained as special cases and the performance of the proposed estimator is investigated by a numerical study.

KW - Adaptive estimation

KW - Block thresholding

KW - Censored data

KW - Nonparametric estimator of derivative of a density

KW - Primary

KW - Rates of convergence

KW - Secondary

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DO - 10.1016/j.jkss.2011.08.004

M3 - Article

AN - SCOPUS:84858707275

VL - 41

SP - 199

EP - 211

JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

SN - 1226-3192

IS - 2

ER -

Wavelet based estimation for the derivative of a density by block thresholding under random censorship

Abstract

Keywords

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