Restricted estimation methods in generalized linear models

Multicollinearity has been shown to have a detrimental effect on parameter estimation in generalized linear models (GLMs). The most frequent approach for estimating parameters in GLMs is the maximum likelihood (ML) method, but it is severely affected by the problem of multicollinearity consequently, the variance-covariance matrix of the ML estimator becomes large and prediction is also inefficient. It is, therefore, preferable to employ methods other than ML when there is a problem of multicollinearity among the explanatory variables. In this dissertation, four iterative restricted biased estimators are proposed to address the problem of multicollinearity by imposing exact and stochastic restrictions on the parameters. These are respectively, the r−k class estimator, stochastic restricted Liu estimator, restricted OK estimator, and stochastic restricted OK estimator. The performances of these estimators are evaluated by the numerical illustrations and simulation studies when a response variable belongs to binomial, Poisson, gamma, and negative binomial distributions. The performance evaluation criteria are the scalar mean square error (SMSE), expected mean square error (EMSE), and prediction mean square error (PMSE). The results demonstrated that under certain conditions, the proposed estimators outperformed the ML and many other estimators considered in this study. Key Words: Generalized linear models, Multicollinearity, Exact restrictions, Stochastic restrictions, Binomial distribution, Poisson distribution, Gamma distribution, Negative binomial distribution