A Modification of the Ridge Type Regression Estimators

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.

Artificial Shortages and Strategic Pricing

“…Such manipulations raise thorny questions about the onslaught of deregulation in 1990s and the tenability of our unprecedented trust in the market mechanism. Economic crises in Asia and power crisis in California are amongst many that will evoke a serious debate on the pros and cons of our increased faith in markets (Gangopadhyay and Chatterji, 2005;El-Salam, 2011). This note offers a simple scheme of strategic pricing for a monopolist who creates artificial shortages to manipulate future prices.…”

On Comparison of Some Ridge Parameters in Ridge Regression

“…Recently, Fallah and Salam, [7] introduce an alternative shrinkage estimator, called modified unbiased ridge (MUR) estimator. This estimator is obtained from Unbiased Ridge Regression (URR), and stated that the MUR estimator is more efficient and more reliable than OLS, RR, and URR estimators based on Matrix Mean Squared Error (MMSE).…”