Shrinkage estimation strategy in quasi-likelihood models

In this paper we consider the estimation problem for the quasi-likelihood model in presence of non-sample information (NSI). More specifically, we introduce a shrinkage estimation strategy for simultaneous model selection and parameter estimation by using the maximum quasi-likelihood estimates as the benchmark estimator, and define the pretest estimator (PTE), shrinkage estimator (SE) and positive-rule shrinkage estimator (PSE). Furthermore, we apply the lasso-type estimation strategy and compare the relative performance of lasso with the suggested estimators. The shrinkage estimators are shown to be efficient estimators compared to others. When the NSI is true the PTE has less risk compared to shrinkage and lasso estimators.