scholarly journals Functional Laws of the Iterated Logarithm for the Product-Limit Estimator of a Distribution Function Under Random Censorship or Truncation

1990 ◽  
Vol 18 (1) ◽  
pp. 160-189 ◽  
Author(s):  
Ming Gao Gu ◽  
Tze Leung Lai
Keyword(s):  
Distribution Function ◽  
Random Censorship ◽  
Iterated Logarithm ◽  
Product Limit Estimator ◽  
Product Limit

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).

Sign in / Sign up

Export Citation Format

Share Document