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SOME ASYMPTOTIC PROPERTIES OF THE SIMPLE LOGLINEAR MODEL
Author(s) -
Maller R. A.
Publication year - 1986
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1986.tb00583.x
Subject(s) - mathematics , deviance (statistics) , asymptotic distribution , log linear model , statistics , poisson distribution , exponential family , estimator , linear model
Summary Consistency and asymptotic normality of the maximum likelihood estimator of β in the loglinear model E(y i ) = e α+β X i , where y i are independent Poisson observations, 1 i aa n , are proved under conditions which are near necessary and sufficient. The asymptotic distribution of the deviance test for β=β 0 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.