Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem
| dc.creator | Buot, Max-Louis G. | |
| dc.creator | Hosten, Serkan | |
| dc.creator | Richards, Donald St. P. | |
| dc.date | 2007-09-06 | |
| dc.date.accessioned | 2026-07-07T08:28:07Z | |
| dc.date.available | 2026-07-07T08:28:07Z | |
| dc.description | Let $μ$ be a $p$-dimensional vector, and let $Σ_1$ and $Σ_2$ be $p \times p$ 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 shall 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. | |
| dc.description | To appear in Statistica Sinica | |
| dc.identifier | https://arxiv.org/abs/0709.0957 | |
| dc.identifier | http://arxiv.org/abs/0709.0957 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/137503 | |
| dc.subject | Statistics Theory | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Computation | |
| dc.subject | 62F99; 14Q99 | |
| dc.title | Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem | |
| dc.type | text |