## Abstract

Let μ be a p-dimensional vector, and let Σ_{1} and Σ_{2} be p × p positive definite covariance matrices. On being given random samples of sizes N_{1} and N_{2} from independent multivariate normal populations N_{p}(μ, Σ_{1}) and N_{p}(μ, Σ_{2}), respectively, the Behrens-Fisher problem is to solve the likelihood equations for estimating the unknown parameters μ, Σ_{1}, and Σ_{2}. We prove that for N_{1}, N_{2} > p there are, almost surely, exactly 2p + 1 complex solutions of the likelihood equations. For the case in which p = 2, we utilize Monte Carlo simulation to estimate the relative frequency with which a typical Behrens-Fisher problem has multiple real solutions; we find that multiple real solutions occur infrequently.

Original language | English (US) |
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Pages (from-to) | 1343-1354 |

Number of pages | 12 |

Journal | Statistica Sinica |

Volume | 17 |

Issue number | 4 |

State | Published - Oct 1 2007 |

## All Science Journal Classification (ASJC) codes

- Statistics and Probability
- Statistics, Probability and Uncertainty