In this article we have considered the problem of prediction within and outside the sample for actual and average values of the study variables in case of ordinary least squares and ridge regression estimators. Finally, the performance properties of the estimators are analyzed. | Yugoslav Journal of Operations Research 27 (2017), Number 2, 243–247 DOI: PREDICTIVE EFFICIENCY OF RIDGE REGRESSION ESTIMATOR Manoj TIWARI Department of Statistics, Panjab University, Chandigarh - 160 014, INDIA mantiwa@ Amit SHARMA Department of Statistics, University of Jammu, Jammu - 180 001, INDIA amitstat99@ Received: January 2017 / Accepted: May 2017 Abstract: In this article we have considered the problem of prediction within and outside the sample for actual and average values of the study variables in case of ordinary least squares and ridge regression estimators. Finally, the performance properties of the estimators are analyzed. Keywords: Linear Regression Model, Ridge Regression Estimator, Least Squares Predictor, Rdge Regression Predictor, Prediction Within and Outside Sample, Prior non-sample Information. MSC: 62J05, 62J07. 1. INTRODUCTION The main aim of a linear regression model is to make prediction, either for the actual values or average values of the study variable; see., Rao and Toutenburg [4] for an interesting account. In both the cases, the estimated equation derived from least squares estimation of parameters provides the best linear unbiased predictions. If unbiasedness is not crucial and can be dropped, several shrinkage estimators are available which may bring substantial gain in precision at the cost of little bias. For example, the method of ridge regression see., Hoerl and Kennard [1],[2] provides an estimator, though biased, which has smaller mean square error than that obtained by the method of least squares. In addition to predicting 244 M. Tiwari, A. Sharma / Predicitive Efficiency of Ridge Regression Estimator average and actual values of a study variable within the sample, one may be interested in knowing performance when the aim is to predict the values outside the sample, for example for the purpose of forecasting and policy prescriptions. In the present paper, an
