Goodness of fit for generalized shrinkage estimation

Cheng, C.-L.; Shalabh; Chaturvedi, A.

doi:10.1090/tpms/1106

Goodness of fit for generalized shrinkage estimation

Authors: C.-L. Cheng, Shalabh and A. Chaturvedi
Journal: Theor. Probability and Math. Statist. 100 (2020), 191-214
MSC (2010): Primary 62J07, 62J05
DOI: https://doi.org/10.1090/tpms/1106
Published electronically: August 5, 2020
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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 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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