Abstract

Researchers in many fields including biomedical often make statistical inferences involving the analysis of count data that exhibit a substantially large proportion of zeros.  Subjects in such research are broadly categorized into  low-risk group that produces only zero counts and high-risk group  leading to counts that can be modeled by a standard Poisson regression model.  The aim of this study is to estimate the model parameters in presence of covariates, some of which may not have significant effects on the magnitude of the counts in  presence of a large proportion of zeros.  The estimation procedures we propose for the study are the pretest, shrinkage, and penalty when some of the covariates may be subject to certain restrictions. Properties of the pretest and shrinkage estimators are discussed in terms of the asymptotic distributional biases and risks. We show that if the dimension of parameters exceeds two, the risk of the shrinkage estimator is strictly less than that of the maximum likelihood estimator, and the risk of the pretest estimator depends on the validity of the restrictions on parameters.   A Monte Carlo simulation study shows that the mean squared errors (MSE)  of shrinkage estimator are comparable to the MSE of the penalty estimators and in particular it performs better than the penalty estimators when the dimension of the restricted parameter space is large. For illustrative purposes, the methods are applied to a real life data set

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