Effect of jackknifing on various ridge type estimators

Article type: Research Article

Authors: Mahmood Batah, Feras Sh.^{a; *} | Gore, S.D.^a | Verma, Med Ram^b

Affiliations: [a] Department of Statistics, Pune University, Ganeshkhind, Pune 411007, India | [b] Division of Agricultural Economics and Statistics, ICAR Research Complex for NEH Region, Umiam (Barapani), Meghalaya 793103, India

Correspondence: [*] Corresponding author: F.Sh. Mahmood Batah, E-mail: [email protected].

Abstract: The paper considers various adhoc assumptions to estimate the ridge parameter k, when the mean squared error (MSE) of ridge estimator is less than the ordinary least squares (OLS) estimator. We consider the optimal ridge parameter k in the jackknife technique applied in the ridge regression, which has not been done before. Two stages are involved in the present study. First is a comparison of the two estimators of the jackknifed ridge regression (JRR) and generalized ridge regression (GRR) with the OLS, in terms of the mean squared error. The ridge parameter k used is nonstochastic in the JRR and GRR estimators. Second is an empirical study of the jackknifed ordinary ridge regression (JORR) properties. Present study concludes with a numerical illustration.

Keywords: Jackknifed ridge estimator, least squares estimator, mean squared error, multicollinearity, ridge regression estimator

DOI: 10.3233/MAS-2008-3304

Journal: Model Assisted Statistics and Applications, vol. 3, no. 3, pp. 201-210, 2008