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In this study, we propose shrinkage methods based on {it generalized ridge regression} (GRR) estimation which is suitable for both multicollinearity and high dimensional problems with small number of samples (large $p$, small $n$). Also, it is obtained theoretical properties of the proposed estimators for Low/High Dimensional cases. Furthermore, the performance of the listed estimators is demonstrated by both simulation studies and real-data analysis, and compare its performance with existing penalty methods. We show that the proposed methods compare well to competing regularization techniques.
We study asymptotic minimax problems for estimating a $d$-dimensional regression parameter over spheres of growing dimension ($dto infty$). Assuming that the data follows a linear model with Gaussian predictors and errors, we show that ridge regressi
Multivariate linear regressions are widely used statistical tools in many applications to model the associations between multiple related responses and a set of predictors. To infer such associations, it is often of interest to test the structure of
We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require the choic
We consider a re-sampling scheme for estimation of the population parameters in the mixed effects nonlinear regression models of the type use for example in clinical pharmacokinetics, say. We provide an estimation procedure which {it recycles}, via r
In the low-dimensional case, the generalized additive coefficient model (GACM) proposed by Xue and Yang [Statist. Sinica 16 (2006) 1423-1446] has been demonstrated to be a powerful tool for studying nonlinear interaction effects of variables. In this