Multiple Regression Analysis of a Poisson Process

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Abstract
A multiple regression model based on the Poisson density is discussed. Point estimation by maximum likelihood results in estimating equations which can be solved by iteration based on scoring or on a successively revised weighted least squares estimator. The first round of each iterative process is shown to be BAN, provided that the ordinary least squares estimator is used as the initial condition. A minimum chi-squared estimator, which can be computed directly from sample observations, is derived and shown to be BAN. A consistent estimator of the variance-covariance matrix for each estimation procedure is given.

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