KL–James–Stein shrinkage for Ill-conditioned linear regression

Abstract

Abstract Severe multicollinearity can make ordinary least squares estimates unstable by inflating their variances. This paper proposes a KL–James–Stein estimator for ill-conditioned linear regression by combining the Kibria–Lukman transformation with a James–Stein-type shrinkage factor. The bias, covariance, matrix mean squared error, and scalar mean squared error of the estimator are derived and compared with those of existing biased estimators. Monte Carlo simulations are used to examine finite-sample performance under different sample sizes, error variances, and levels of correlation among the regressors. The results show that the proposed estimator often attains smaller scalar mean squared error, especially when collinearity is strong. Two empirical applications, based on the Portland cement and Boston housing datasets, provide further evidence on its practical behavior. Overall, the KL–JSE estimator offers a competitive alternative for ill-conditioned regression problems, although its gains depend on the design structure and the resulting bias–variance trade-off.