SOME ASYMPTOTIC PROPERTIES OF THE SIMPLE LOGLINEAR MODEL |
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Authors: | R. A. Maller |
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Affiliation: | CSIRO Division of Mathematics arid Statistics, Australia |
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Abstract: | Consistency and asymptotic normality of the maximum likelihood estimator of β in the loglinear model E(yi) = eα+βXi, where yi are independent Poisson observations, 1 iaan, are proved under conditions which are near necessary and sufficient. The asymptotic distribution of the deviance test for β=β0 is shown to be chi-squared with 1 degree of freedom under the same conditions, and a second order correction to the deviance is derived. The exponential model for censored survival data is also treated by the same methods. |
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