Generalized Multivariate Ridge Regression Estimate and Criteria Q(c)for Choosing Matrix K

When multicollinearity is present in a set of the regression variables, the least square estimate of the regression coefficient tends to be unstable and it may lead to erroneous inference.In this paper, generalized ridge estimate β^*(K) of the regression coefficient β=vec(B) is considered in multivaiale linear regression model. The MSE of the above estimate is less than the MSE of the least square estimate by choosing the ridge parameter matrix K. Moreover, it is pointed out that the Criterion MSE for choosing matrix K of generalized ridge estimate has several weaknesses. In order to overcome these weaknesses, a new family of criteria Q(c) is adpoted which includes the criterion MSE and criterion LS as its special case. The good properties of the criteria Q(c) are proved and discussed from theoretical point of view. The statistical meaning of the scale c is explained and the methods of determining c are also given.