Quantiles of Kaplan-Meier Estimator.

Abstract

The theory of counting processes, martingales and stochastic integration is used to establish in a simple way a Bahadur representation for the quantiles of the Kaplan-Meier estimator. This Bahadur representation is combined with a result of Aalen (1976) to prove the asymptotic independence of the quantile estimates in the competing risks problem. Finally, the theory is used to study the estimates of the quantiles of the life length of a coherent system proposed by Doss, Freitag, and Proschan (1986). Keywords: Quantiles; competing risks problem; Bahadur representation; Kaplan Meier estimator; coherent structure; reliability function; stochastic integral.

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Document Details

Document Type
Technical Report
Publication Date
Nov 04, 1986
Accession Number
ADA175050

Entities

People

  • Hani Doss
  • Steven Freitag

Organizations

  • Stanford University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Asymptotic Normality
  • Confidence Limits
  • Convergence
  • Covariance
  • Data Science
  • Distribution Functions
  • Estimators
  • Gaussian Processes
  • Information Science
  • Integrals
  • Intervals
  • Mathematical Analysis
  • Probability
  • Random Variables
  • Statistics
  • United States
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Statistical inference.