General Coverage Problems with Applications, and Bootstrap Method in Survival Analysis and Reliability Theory.

Abstract

By approximating the classical Product-Limit estimator of a distribution function with an average of lid random variables, we derive, for the first time in the literature, sufficient and necessary conditions for the rates of (both strong as well as weak laws) uniform convergence of the Product-Limit estimator over the whole line. These findings somehow fill a longstanding gap in the theory of Survival Analysis and provide a systematic tool handling other challenging problems when data are incomplete. In deriving our main results we also suggested a heurestic way of estimating the rates of convergence. To demonstrate its applications we prove a related conjecture of Gill and explain how a reliable confidence interval and band near the endpoint can be constructed.

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Document Details

Document Type
Technical Report
Publication Date
Jan 08, 1998
Accession Number
ADA337421

Entities

People

  • Shaw-hwa Lo

Organizations

  • Columbia University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Abstracts
  • Accuracy
  • Base Lines
  • Cancer
  • Convergence
  • D Band
  • Diseases And Disorders
  • Estimators
  • Lung Cancer
  • Probability
  • Random Variables
  • Reliability
  • Statistics
  • Students
  • Survival
  • Theses
  • Weak Convergence

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Regression Analysis.
  • Theoretical Analysis.