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Estimation and Testing in Poisson Regression Models with Over-Dispersion

机译：具有过度色散的泊松回归模型的估计和检验

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Poisson regression models with over-dispersion are considered. Over-dispersion is modeled by introducing stochastic variables Z(sub i) such that the dependent variable Y(sub i) given Z(sub i) = z(sub i) is Poisson distributed, with expectation mu(sub i)z(sub i) where mu(sub i) depends on covariates x(sub ij) through a link function g, g(mu(sub i)) = Summation over j of beta(sub j) x(sub ij). The usual iteration procedure for estimation can be modified. Given square root of n-consistent initial estimators for beta and lambda = var(Z(sub i)) one iteration step of the new procedure is needed for the desired asymptotic normality, under quite mild conditions. The construction of square root of n-consistent initial estimators of beta and lambda is considered. For testing the null hypothesis that a number of elements of beta is zero, a Wald-statistic is proposed as test-statistic.

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