Abstract
Problem statement: Many regression estimators have been used to remedy multicollinearity problem. The ridge estimator has been the most popular one. However, the obtained estimate is biased. Approach: In this stuyd, we introduce an alternative shrinkage estimator, called modified unbiased ridge (MUR) estimator for coping with multicollinearity problem. This estimator is obtained from Unbiased Ridge Regression (URR) in the same way that Ordinary Ridge Regression (ORR) is obtained from Ordinary Least Squares (OLS). Properties of MUR estimator are derived. Results: The empirical study indicated that the MUR estimator is more efficient and more reliable than other estimators based on Matrix Mean Squared Error (MMSE).Conclusion: In order to solve the multicollinearity problem, the MUR estimator was recommended.
Highlights
Consider the following linear regression model: Y = Xβ + Є (1)2010; Rana et al, 2009)
The data was used by Course et al (1995) to compare Scalar Mean squared Error (SMSE) performance of Unbiased Ridge Regression (URR), Ordinary Ridge Regression (ORR) and Ordinary Least Squares (OLS)
We use this data to illustrate the performance of the Modified Unbiased Ridge (MUR) estimator to the OLS, ORR and URR estimators to compare the Matrix Mean Squared Error (MMSE) performance of these estimators
Summary
Consider the following linear regression model: Y = Xβ + Є (1). 2010; Rana et al, 2009). Swinded (1976) defined Modified Ridge Regression (MRR) estimator as follows: β(k, b) = (X 'X + KIp )−1(X 'Y + Kb), K ≥ 0 (4). If X’X is singular or near where, b is a prior estimate of β. As K increases indefinitely, the MRR estimator approaches b. Crouse et al (1995) defined the Unbiased Ridge Regression (URR) estimator as follows: β(k, j) = (X 'X + KIp )−1(X 'Y + Kj), K ≥ 0
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