Abstract
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 situations, known and unknown. The goodness-of-fit statistics based on the idea of coefficient of determination in a 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.
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