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‰Α“‘Œ«Œεi“Œ‹ž‘εŠw‘εŠw‰@ŒoΟŠwŒ€‹†‰Θj
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On the degrees of freedom in the shrinkage estimation
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We study the degrees of freedom in the shrikage estimation of the regression coefficients. Generalizing the idea of the Lasso, we consider the problem of estimating the coefficients by the projection of the OLS estimator onto a closed convex set. Then an unbiased estimator of the degrees of freedom is derived in terms of geometric quantities under a smoothness condition on the boundary of the closed convex set. As an application, we obtain a $C_p$ type criterion and AIC for selecting the tunig parameter.