Improving the estimators of the parameters of a probit regression model: A ridge regression approach

This paper considered the estimation of the regression parameters of a general probit regression model. Accordingly, we proposed five ridge regression (RR) estimators for the probit regression models for estimating the parameters (β)(β) when the weighted design matrix is ill-conditioned and it is suspected that the parameter ββ may belong to a linear subspace defined by Hβ=hHβ=h. Asymptotic properties of the estimators are studied with respect to quadratic biases, MSE matrices and quadratic risks. The regions of optimality of the proposed estimators are determined based on the quadratic risks. Some relative efficiency tables and risk graphs are provided to illustrate the numerical comparison of the estimators. We conclude that when q≥3q≥3, one would uses PRRRE; otherwise one uses PTRRE with some optimum size αα. We also discuss the performance of the proposed estimators compare to the alternative ridge regression method due to Liu (1993).