On Stochastic Linear Regression Model Selection

The research article primarily focuses on the criteria for selecting best stochastic linear regression model namely Cp conditional mean square error prediction, Generalized Mean Squared Error criterion (GMSE) which comes out of the deficiencies of R 2 and R 2 criteria. The most uncomfortable aspect of both R 2 and R 2 measures is that they do not include a consideration of losses associated with choosing an incorrect model. C.L.Cheng et al, in 2014, in their research paper proposed the goodness of fit statistics based on the variants of R 2 for multiple measurement errors and also studied the asymptotic properties of the conventional R 2 and the proposed variants of R 2 like goodness of fit statistics analytically and numerically. M.HasheemPesaran et al, in 1994, in their paper discussed why both R 2 and R 2 are inappropriate as a measure of fit and for model selection in the sense that their use does not guarantee that true model is chosen even asymptotically.D.Wallach et.al, in 1987, in their paper used the mean square error of prediction (MSEP) as a criterion for evaluating models for studying ecological and agronomic systems. M.Revan Ozkale, in 2009, in his paper introduced a new estimator by combining ideas underlying the mined and the ridge regression estimators under the assumption that the errors are not independent and identically distributes when there are stochastic linear restrictions on the parameter vector. David A. Mc Allester, in 2003, in his article, gave a PACBayesian performance guarantee for stochastic model selection that is superior to analogous guarantees for deterministic model selection.