A restricted Liu estimator for binary regression models and its application to an applied demand system

摘要

In this article, we propose a restricted Liu regression estimator (RLRE) for estimating the parameter vector, beta, in the presence of multicollinearity, when the dependent variable is binary and it is suspected that beta may belong to a linear subspace defined by R beta = r. First, we investigate the mean squared error (MSE) properties of the new estimator and compare them with those of the restricted maximum likelihood estimator (RMLE). Then we suggest some estimators of the shrinkage parameter, and a simulation study is conducted to compare the performance of the different estimators. Finally, we show the benefit of using RLRE instead of RMLE when estimating how changes in price affect consumer demand for a specific product.