Comparison of ridge and other shrinkage estimation techniques

• Main Author: Vumbukani, Bokang C
• Other Authors: Thiart, Christien
• Format: Dissertation
• Language: English
• Published: University of Cape Town 2014
• Subjects: Statistical Sciences
• Online Access: http://hdl.handle.net/11427/4364

Includes bibliographical references. === Shrinkage estimation is an increasingly popular class of biased parameter estimation techniques, vital when the columns of the matrix of independent variables X exhibit dependencies or near dependencies. These dependencies often lead to serious problems in least squares estimation: inflated variances and mean squared errors of estimates unstable coefficients, imprecision and improper estimation. Shrinkage methods allow for a little bias and at the same time introduce smaller mean squared error and variances for the biased estimators, compared to those of unbiased estimators. However, shrinkage methods are based on the shrinkage factor, of which estimation depends on the unknown values, often computed from the OLS solution. We argue that the instability of OLS estimates may have an adverse effect on performance of shrinkage estimators. Hence a new method for estimating the shrinkage factors is proposed and applied on ridge and generalized ridge regression. We propose that the new shrinkage factors should be based on the principal components instead of the unstable OLS estimates.