Ridge Analysis Following a Preliminary Test of the Shrunken Hypothesis

Abstract RIDGE ANALYSIS is of interest when some generalized Ridge regression coefficient vectors are significantly more likely to have Mean Squared Error (MSE) optimality properties than is any uniformly SHRUNKEN version of the ordinary least squares estimator. The normal distribution theory likelihood ratio statistic for the corresponding composite hypothesis is derived, and a small sample F-test is shown to be conservative. The asymptotic distribution of the likelihood ratio provides a large sample test of the RISE optimality of any restricted Ridge FAMILY of solutions. The likelihood approach for solution selection WITHIN a given family is then compared and contrasted with some snggestions of Mallows 8 and Allen 1 and with a new, non-stochastic criterion, SSCBC. KEY WORDS: Generalized Ridge RegressionLikelihood of Mean Sqllared Error OptimalitySkun of Squares of Correlations Between CoefficientsRelative Magnitudes and Signs of CoefficientsEfrects of Rescalings/lieparnmeterizations