## Abstract

We assume a random sample of n + 1 from a MVNK(μ,∑) distribution and study the test statistics for H_{0} : ∑= ∑_{0} versus Hi : E ≥ E_{0} and H1 : ∑≥ ∑_{0} versus H_{2} : ∑ ≠∑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 language | English (US) |
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Pages (from-to) | 3121-3140 |

Number of pages | 20 |

Journal | Communications in Statistics - Theory and Methods |

Volume | 23 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1994 |

## Keywords

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

## ASJC Scopus subject areas

- Statistics and Probability