The Product-Limit Estimate as an Inverse-Probability-Weighted Average

Shen, Pao‐Sheng

doi:10.1081/sta-120021323

Cited by 33 publications

(30 citation statements)

References 15 publications

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“…The following theorem shows thatŜ P andĜ P also satisfy selfconsistent equations (11) and (12), respectively.…”

Section: Introductionmentioning

confidence: 90%

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Nonparametric estimation with left-truncated and right-censored data when the sample size before truncation is known

Shen

2012

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In this article, we consider nonparametric estimation of the survival function when the data are subject to left-truncation and right-censoring and the sample size before truncation is known. We propose two estimators. The first estimator is derived based on a self-consistent estimating equation. The second estimator is obtained by using the constrained expectation-maximization algorithm. Simulation results indicate that both estimators are more efficient than the product-limit estimator. When there is no censoring, the performance of the proposed estimators is compared with that of the estimator proposed by Li and Qin [Semiparametric likelihood-based inference for biased and truncated data when total sample size is known, J. R. Stat. Soc. B 60 (1998), pp. 243-254] via simulation study.

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“…The following theorem shows thatŜ P andĜ P also satisfy selfconsistent equations (11) and (12), respectively.…”

Section: Introductionmentioning

confidence: 90%

“…Theorem 2 When there is no censoring, the NPMLEsŜ P andĜ P satisfy Equations (11) and (12), respectively.…”

Section: Introductionmentioning

confidence: 97%

Nonparametric estimation with left-truncated and right-censored data when the sample size before truncation is known

Shen

2012

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“…For random censoring model, Satten and Datta (2001) showed that the Kaplan and Meier (1958) estimator of F(t) can be expressed as an IPW average (see Robins 1993;Robins and Finkelstein 2000). For the univariate random truncation and censoring model, Shen (2003) showed that the truncation nonparametric maximum likelihood estimator (NPMLE) (see Woodroofe 1985) and the censoring-truncation NPMLE (see Wang 1987) of survival function can also be expressed as IPW averages. For the twice censored data described in Sect.…”

Section: Proposed Estimatormentioning

confidence: 98%

Nonparametric estimators of the survival function with twice censored data

Shen

2010

Ann Inst Stat Math

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“…For the univariate random truncation and censoring model, Shen (2003) showed that the truncation NPMLE (see Woodroofe 1985) and the censoring-truncation NPMLE (see Wang 1987) of survival function can also be expressed as IPW averages. For double-truncated data, the following arguments provide the motivation for using IPW estimators.…”

Section: Inverse-probability-weighted (Ipw) Estimatormentioning

confidence: 99%