Consistent ridge estimation for replicated ultrastructural measurement error models

Abstract

The presence of measurement errors in data and multicollinearity among the explanatory variables have negative effects on the estimation of regression coefficients. Within this respect, the motivation of this article is to examine measurement errors and multicollinearity problems simultaneously. In this paper, by utilizing three different forms of corrected score functions three consistent ridge regression estimators are proposed. Theoretical comparisons of these new estimators are examined by implementing the mean squared error criterion. Large sample properties of these estimators are investigated without assuming any distributional assumption. Two numerical examples are presented using real data sets and also a simulation study is performed. The findings indicate that the newly proposed three estimators outperform the existing estimators by the criterion of mean squared error.