Abstract
A large amount of literature has been developed for the presence of multicollinearity among the explanatory variables that are often performed with the aim of reducing the undesirable effects on the maximum likelihood estimate(MLE). In particular, many authors have discussed ridge estimation (RE) under the framework of the mean regression model, because the RE enjoys the advantage that its mean squared error (MSE) is less than that of MLE. However, most of the existing methods assume or are applicable to symmetrical data. In this paper, we consider the case of skewed (or asymmetrical) data, which often occur in practice and include symmetrical data as a special case, and derive the RE of the skew-mormal mode regression model under multicollinearity problem. A maximum likelihood method via an EM algorithm and the eleven ridge parameter methods are investigated. Monte Carlo simulation results indicate that the suggested estimator performs better than the MLE in terms of MSE. Then proposed methods are illustrated by a real data analysis.
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