A Comparative Study on the Performance of New Ridge Estimators

Abstract

Least square estimators in multiple linear regressions under multicollinearity become unstable as they produce large variance for the estimated regression coefficients. Hoerl and Kennard 1970, developed ridge estimators for cases of high degree of collinearity. In ridge estimation, the estimation of ridge parameter ( k ) is vital. In this article new methods for estimating ridge parameter are introduced. The performance of the proposed estimators is investigated through mean square errors (MSE). Monte-Carlo simulation technique indicated that the proposed estimators perform better than ordinary least squares (OLS) estimators as well as few other ridge estimators.

The Performance Of Some Biased Estimators With Different Biased Parameter In Linear Regression Model

“…The results of the simulation are seen in Tables (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12). the results were analyzed by splitting the results into two sections as follow:…”

Performance of Ridge Estimators Based on Weighted Geometric Mean and Harmonic Mean

“…Further for large n, say n ≥ 50, low error variance σ 2 (≤ 5), low and moderate degree of correlations (ρ), all the estimators considered here have produced unstable estimates for the ridge parameter. Estimators due to k 1 i.e., Hoerl et al [18], Satish and Vidya [20,21,24] i.e., k 7 , k 8 and k 9 behaved better, and yielded more stable estimates to the regression coefficients, but it is observed carefully that, these estimators slightly over shrinks the estimates to the regression coefficients as compared to other estimators due to Dorugade and Kashid [15], Satish and Vidya [24] i.e., k 10 , k 11, and, k 12 ; and the proposed estimators k 13 and k 14 .…”

“…, is the second largest eigen value of X"X matrix. It is observed that the estimators defined in equations (7) to (12) are verified under very high degree (ρ ≥ 0.9) of multicollinearity between the predictors whereas, the estimators due to Satish and Vidya [20,21,24] are investigated under various degree of multicollinearity viz., low, moderate and high degree of multicollinearity. Also, Satish and Vidya [20,24], have considered different error distributions viz., normal and non-normal (t (5) -distribution with 5 d.f.)…”

Alternative Ridge Parameters in Linear Model

“…Different techniques for estimating the ridge parameters have been developed in literature. These include those proposed by Hoerl and Kennard (1970), McDonald and Galarneau (1975), Lawless and Wang (1976), Dempster et al (1977), Gibbons (1981), Kibria (2003), Khalaf and Shukur (2005), Alkhamisi et al (2006), Alkhamisi and Shukur (2008), Batach et al (2008), Muniz and Kibria (2009), Dorugade and Kashid (2010), Mansson et al (2010), Khalaf (2013), Ghadhan and Mohamed (2014), Kibria and Shipra (2016), Bhat (2016), Lukman and Ayinde (2017), Fayose and Ayinde (2019). Algama (2018a) proposed methods of selecting biasing parameters in Generalized Linear Models (GLM) and also in Algama (2018b) some modified versions of ridge parameter estimators for gamma models were proposed.…”