Statistical Inference for Bounds of Random Variables

Abstract

Robson and Whitlock (1964) considered point estimation and confidence limits for the upper bound of a random variable when the bound was known to be a truncation point. However, their approach to the point estimation problem failed to produce an estimator with smaller mean squared error than the largest order statistic from a random sample. In this paper we will construct point estimators of the bounds of random variables which are substantially better estimators than the extreme order statistics for many classes of random variables, including those whose distributions are truncated at one or both ends. We will also construct confidence limits and tests of hypotheses for bounds. The main results are large sample results.

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Document Details

Document Type
Technical Report
Publication Date
Apr 03, 1979
Accession Number
ADA069180

Entities

People

  • Peter Cooke

Organizations

  • Stanford University

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Classification
  • Confidence Limits
  • Data Science
  • Distribution Functions
  • Hypotheses
  • Information Science
  • Military Research
  • Order Statistics
  • Probability
  • Random Variables
  • Security
  • Statistical Algorithms
  • Statistical Inference
  • Statistical Samples
  • Statistics
  • Truncation

Fields of Study

  • Mathematics

Readers

  • Statistical inference.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms