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Theory of Probability and Mathematical Statistics



Goodness of fit for generalized shrinkage estimation

C.-L. Cheng, Shalabh, A. Chaturvedi

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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 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.

Keywords: Linear regression, non-spherical disturbances, coefficient of determination (R2), shrinkage estimation, generalized least squares estimator, feasible double k-class estimators, feasible generalized least squares estimator, double k-class estimators, goodness of fit.

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