Mathematics – Statistics Theory
Scientific paper
2007-09-06
Mathematics
Statistics Theory
To appear in Statistica Sinica
Scientific paper
Let $\mu$ be a $p$-dimensional vector, and let $\Sigma_1$ and $\Sigma_2$ 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 $N_p(\mu,\Sigma_1)$ and $N_p(\mu,\Sigma_2)$, respectively, the Behrens-Fisher problem is to solve the likelihood equations for estimating the unknown parameters $\mu$, $\Sigma_1$, and $\Sigma_2$. 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.
Buot Max-Louis G.
Hosten Serkan
Richards Donald St. P.
No associations
LandOfFree
Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Counting and Locating the Solutions of Polynomial Systems of Maximum Likelihood Equations, II: The Behrens-Fisher Problem will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-466579