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ABSTRACT In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family… Click to show full abstract
ABSTRACT In this paper, assuming that there exist omitted explanatory variables in the specified model, we derive the exact formula for the mean squared error (MSE) of a general family of shrinkage estimators for each individual regression coefficient. It is shown analytically that when our concern is to estimate each individual regression coefficient, the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators under some conditions even when the relevant regressors are omitted. Also, by numerical evaluations, we showed the effects of our theorem for several specific cases. It is shown that the positive-part shrinkage estimators have smaller MSE than the original shrinkage estimators for wide region of parameter space even when there exist omitted variables in the specified model.
Journal Title: Journal of Statistical Computation and Simulation
Year Published: 2018
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