A semiparametric generalized ridge estimator and link with model averaging

Abstract

In recent years, the suggestion of combining models as an alternative to selecting a single model from a frequentist prospective has been advanced in a number of studies. In this paper, we propose a new semi-parametric estimator of regression coe¢ cients, which is in the form of a feasible generalized ridge estimator by Hoerl and Kennard (1970b) but with di¤erent biasing factors. We prove that the generalized ridge estimator is algebraically identical to the model average estimator. Further, the biasing factors that determine the properties of both the generalized ridge and semi-parametric estimators are directly linked to the weights used in model averaging. These are interesting results for the interpretations and applications of both semi-parametric and ridge estimators. Furthermore, we demonstrate that these estimators based on model averaging weights can have properties superior to the well-known feasible generalized ridge estimator in a large region of the parameter space. Two empirical examples are presented.

Bootstrapping the Stein-Rule Estimators

“…Recently, shrinkage estimators are applied to several general models [see e.g., (Hansen 2016a(Hansen , 2017]. Also, it is well known some recent techniques including LASSO, SCAD and model averaging can be considered as kinds of shrinkage estimation [see, e.g., Fan and Li (2001), Hansen (2016b), Tibshirani (1996), Ullah et al (2016) and Zou (2006)]. In particular, extending the idea of Hausman (1978) pre-test in Guggenberger (2010), Hansen (2017) proposed an estimator which consists of the ordinary least squares estimator and the two-stage least squares estimator under the assumption that the correlation coefficient is local to zero.…”