The strong representation for the nonparametric estimator of length-biased and right-censored data

Jianhua Shi; Xiaoping Chen; Yong Zhou

doi:10.1016/j.spl.2015.04.029

The strong representation for the nonparametric estimator of length-biased and right-censored data

Jianhua Shi
, Xiaoping Chen^*
, Yong Zhou

^*Corresponding author for this work

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

5 Scopus citations

Abstract

In this paper, we consider the modified product-limit estimator of an unknown distribution function proposed by Huang and Qin (2011), where the observations are subject to length-biased and right-censored data. A strong representation for the modified product-limit estimator is established with a remainder O(n-3/4(logn)3/4) a.s. Such results are very useful when we consider statistics that are the function of the estimator of nonparametric distribution function. Also, a uniform consistency rate of the estimator is given.

Original language	English
Pages (from-to)	49-57
Number of pages	9
Journal	Statistics and Probability Letters
Volume	104
DOIs	https://doi.org/10.1016/j.spl.2015.04.029
State	Published - 2015
Externally published	Yes

Keywords

Length-biased
Right-censored
Strong representation
Truncated data

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10.1016/j.spl.2015.04.029

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title = "The strong representation for the nonparametric estimator of length-biased and right-censored data",

abstract = "In this paper, we consider the modified product-limit estimator of an unknown distribution function proposed by Huang and Qin (2011), where the observations are subject to length-biased and right-censored data. A strong representation for the modified product-limit estimator is established with a remainder O(n-3/4(logn)3/4) a.s. Such results are very useful when we consider statistics that are the function of the estimator of nonparametric distribution function. Also, a uniform consistency rate of the estimator is given.",

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year = "2015",

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AU - Shi, Jianhua

AU - Chen, Xiaoping

AU - Zhou, Yong

PY - 2015

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N2 - In this paper, we consider the modified product-limit estimator of an unknown distribution function proposed by Huang and Qin (2011), where the observations are subject to length-biased and right-censored data. A strong representation for the modified product-limit estimator is established with a remainder O(n-3/4(logn)3/4) a.s. Such results are very useful when we consider statistics that are the function of the estimator of nonparametric distribution function. Also, a uniform consistency rate of the estimator is given.

AB - In this paper, we consider the modified product-limit estimator of an unknown distribution function proposed by Huang and Qin (2011), where the observations are subject to length-biased and right-censored data. A strong representation for the modified product-limit estimator is established with a remainder O(n-3/4(logn)3/4) a.s. Such results are very useful when we consider statistics that are the function of the estimator of nonparametric distribution function. Also, a uniform consistency rate of the estimator is given.

KW - Length-biased

KW - Right-censored

KW - Strong representation

KW - Truncated data

UR - https://www.scopus.com/pages/publications/84929627305

U2 - 10.1016/j.spl.2015.04.029

DO - 10.1016/j.spl.2015.04.029

M3 - 文章

AN - SCOPUS:84929627305

SN - 0167-7152

VL - 104

SP - 49

EP - 57

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

The strong representation for the nonparametric estimator of length-biased and right-censored data

Abstract

Keywords

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