One-sided test of a covariance matrix with a known null value

James Arthur Calvin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We assume a random sample of n + 1 from a MVNK(μ,∑) distribution and study the test statistics for H0 : ∑= ∑0 versus Hi : E ≥ E0 and H1 : ∑≥ ∑0 versus H2 : ∑ ≠∑0, where ∑0 is known. Estimation of ∑ is based on maximizing the likelihood of the location invariant sufficient statistic 5, the sample covariance matrix. The one-sided nature of the hypotheses leads to a restricted parameter space and the use of techniques from order restricted inference. The asymptotic distributions of the resulting test statistics are derived and shown to be a poor approximation for small to moderate size samples. An empirical distribution approach is suggested and the power of the tests is discussed.

Original languageEnglish (US)
Pages (from-to)3121-3140
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Issue number11
StatePublished - Jan 1 1994


  • Chi-bar square distribution
  • Order restricted inference
  • quality control
  • restricted maximum likelihood estimation
  • variance components

ASJC Scopus subject areas

  • Statistics and Probability


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