Effect of Some Estimators on a Large Sample Approximation to the Non-Null Distribution of the Pearson Chi-Square Statistic.

Abstract

In this paper three distinct formulations of the Pearson chi-square test statistic, each of which employs random interval boundaries, are considered in presenting an answer to the following problem: Given a finite sample size and specified fixed composite null and alternative hypotheses, which method of estimation of the unknown parameters leads to a test which is most sensitive to departures from the null hypothesis in the direction of the fixed alternative? The proposed answer is based on a finite sample size approximation to the distribution of the appropriate quadratic form under the alternative hypothesis. Key words: Pearson chi-square test, Test of fit, Asymptotic distribution.

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Document Details

Document Type
Technical Report
Publication Date
Feb 01, 1985
Accession Number
ADA153515

Entities

People

  • A. E. Muhly
  • J. Gurland

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Advanced Electronics
  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Chi Square Test
  • Composite Materials
  • Data Science
  • Distribution Functions
  • Hypotheses
  • Information Science
  • Intervals
  • Mathematics
  • Probability
  • Random Variables
  • Sequences
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Statistical inference.
  • Systems Analysis and Design