Consistency of Invariants for the Multivariate Analysis of Variance

Abstract

Two notions of consistency of invariant tests for tbe MANOVA testing problems are examined and compared: sample size consistency (the classical notion) and parameter consistency, which requires chat for fixed sample size, the power of the test approaches one for any sequence of alternatives whose distance from the null hypothesis approaches infinity. The Roy, Lawley-Hotelling, and likelihood ratio (Wilks criterion) tests are consistent in both senses, whereas the Bartlett-Nanda-Pillai trace test, although sample size consistent, is not parameter consistent unless the significance level a or the error degrees of freedom n is sufficiently large.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1987
Accession Number
ADA591103

Entities

People

  • Michael D. Perlman
  • Theodore W. Anderson

Organizations

  • Stanford University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Analysis Of Variance
  • Boundaries
  • California
  • Consistency
  • Contracts
  • Covariance
  • Data Science
  • Information Science
  • Military Research
  • Multivariate Analysis
  • New York
  • Sequences
  • Statistical Algorithms
  • Statistical Analysis
  • Statistical Inference
  • Statistics
  • Universities

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.
  • Regression Analysis.