Maximum likelihood estimation of the poisson distribution of r×c independent samples in the presence of linear constraints on the vector of parameters
David Christopher Gruben · Communication in Statistics- Theory and Methods · 1993
Consider the re independent Poisson samples, whose ijth sample is composed of nij- independent and identically distributed observations from the Poisson (λij) distribution, where the vector is subject to , and where H is an m×rc, matrix of m linear constraints. Maximum likelihood estimators of are derived in terms of the vector of Lagrangian multipliers on the m constraints. There is no closed form solution for these estimators. An algorithm for numerically solving for these estimators is proposed and examined. Tests of hypotheses may be performed based on the likelihood ratio statistic. Approximate estimators of the variance of the maximum likelihood estimators are discussed. An example of the procedure is given.