The Exact General Formulas for the Moments of a Ridge Regression Estimator when the Regression Error Terms Follow a Multivariate t Distribution

Huang (1999 Huang , J. C. ( 1999 ). Improving the estimation precision for a selected parameter in multiple regression analysis: an algebraic approach . Econ. Lett. 62 : 261 – 264 .Crossref], Web of Science ®] , Google Scholar]) proposed a feasible ridge regression (FRR) estimator to estimate a specific regression coefficient. Assuming that the error terms follow a normal distribution, Huang (1999 Huang , J. C. ( 1999 ). Improving the estimation precision for a selected parameter in multiple regression analysis: an algebraic approach . Econ. Lett. 62 : 261 – 264 .Crossref], Web of Science ®] , Google Scholar]) examined the small sample properties of the FRR estimator. In this article, assuming that the error terms follow a multivariate t distribution, we derive an exact general formula for the moments of the FRR estimator to estimate a specific regression coefficient. Using the exact general formula, we obtain exact formulas for the bias, mean squared error (MSE), skewness, and kurtosis of the FRR estimator. Since these formulas are very complex, we compare the bias, MSE, skewness, and kurtosis of the FRR estimator with those of ordinary least square (OLS) estimator by numerical evaluations. Our numerical results show that the range of MSE dominance of the FRR estimator over the OLS estimator is widen under a fat tail distributional assumption.