Goodness of fit for generalized shrinkage estimation

The present paper develops a goodness of fit statistic for the linear regression models fitted by the shrinkage type estimators. A family of double k-class estimators is considered as a shrinkage estimator which encompasses several estimators as its particular case. The covariance matrix of error term is assumed to be a non-identity matrix under two situationsknown and unknown. The goodness of fit statistics based on the idea of coefficient of determination in multiple linear regression model is proposed for the family of double k-class estimators. Its first and second order moments up to the first order of approximation are derived and finite sample properties are studied using the Monte-Carlo simulation.