STRONG EMBEDDING OF PRODUCT–LIMIT ESTIMATOR OF BIVARIATE SURVIVAL DISTRIBUTION FUNCTION UNDER RANDOM CENSORSHIP

1995 ◽  
Vol 15 ◽  
pp. 123-132 ◽  
Author(s):  
Qihua Wang
Keyword(s):  
Distribution Function ◽  
Random Censorship ◽  
Survival Distribution ◽  
Bivariate Survival ◽  
Strong Embedding ◽  
Product Limit Estimator ◽  
Product Limit ◽  
Survival Distribution Function

Estimation of a Distribution Function from Incomplete Observations

1975 ◽  
Vol 12 (S1) ◽  
pp. 67-87 ◽  
Author(s):  
Paul Meier
Keyword(s):  
Distribution Function ◽  
Empirical Distribution Function ◽  
Empirical Distribution ◽  
Random Censoring ◽  
Basic Properties ◽  
Complex Problems ◽  
Product Limit Estimator ◽  
Incomplete Observations ◽  
Product Limit ◽  
Censored Observations

The product-limit estimator for a distribution function, appropriate to observations which are variably censored, was introduced by Kaplan and Meier in 1958; it has provided a basis for study of more complex problems by Cox and by others. Its properties in the case of random censoring have been studied by Efron and later writers. The basic properties of the product-limit estimator are here shown to be closely parallel to the properties of the empirical distribution function in the general case of variably and arbitrarily censored observations.

scholarly journals A presmooth estimator of unbiased distributions with length-biased data

2019 ◽  
Vol 13 (4) ◽  
pp. 317-323
Author(s):  
Reza Heidari ◽  
Vahid Fakoor ◽  
Ali Shariati
Keyword(s):  
Distribution Function ◽  
Statistical Inference ◽  
Strong Consistency ◽  
Simulation Studies ◽  
Finite Sample ◽  
Product Limit Estimator ◽  
Alternative Method ◽  
Product Limit

Abstract In this paper, we propose a presmooth product-limit estimator to draw statistical inference on the unbiased distribution function representing the population of interest. The strong consistency of the estimator proposed is investigated. The finite sample performance of the proposed estimator is evaluated using simulation studies. It is observed that the proposed estimator exhibits greater efficiency in comparison with the alternative method in de Uña-Álvarez (Test 11(1):109–125, 2002).

Estimation of Bivariate Survival Function from Random Censored Data with Poisson Sample Size

2020 ◽  
Vol 72 (2) ◽  
pp. 111-121
Author(s):  
Abdurakhim Akhmedovich Abdushukurov ◽  
Rustamjon Sobitkhonovich Muradov
Keyword(s):  
Relative Risk ◽  
Sample Size ◽  
Censored Data ◽  
Survival Function ◽  
Survival Functions ◽  
Power Structures ◽  
Bivariate Survival ◽  
Empirical Estimates ◽  
Bivariate Survival Function ◽  
Product Limit

At the present time there are several approaches to estimation of survival functions of vectors of lifetimes. However, some of these estimators either are inconsistent or not fully defined in range of joint survival functions and therefore not applicable in practice. In this article, we consider three types of estimates of exponential-hazard, product-limit, and relative-risk power structures for the bivariate survival function, when replacing the number of summands in empirical estimates with a sequence of Poisson random variables. It is shown that these estimates are asymptotically equivalent. AMS 2000 subject classification: 62N01

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