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On Liu-type biased estimators in measurement error models

ABSTRACT This paper considers the shrinkage estimation of parameters of measurement error models when it is suspected that the parameters may belong to a linear subspace. The class of Liu type estimators is proposed by choosing five quasi-empirical Bayes estimators in the presence of measurement errors in the data. This class of estimator combines the sample and prior information together along with the good properties of ridge estimators and chosen five quasi-empirical Bayes estimators. The advantages of the proposed class of estimators over the classical ridge regression estimator is that the quasi-empirical Bayes estimators are a linear function of the tuning parameter. When data has problems of measurement errors and multicollinearity, then these estimators can handle both the issues simultaneously. The asymptotic properties of the estimators are derived and analyzed. A Monte Carlo simulation is conducted and its findings are reported.