Utilizing stochastic prior information for replicated ultrastructural measurement error models in case of multicollinearity

The appearance of measurement errors and multicollinearity in data are two problematic issues that adversely affect the estimation of regression coefficients. In such circumstances, concerning regression coefficients, it can be practicable to utilize some prior information in the type of stochastic linear restrictions. The main purpose of this article is to overcome the problems of measurement errors and multicollinearity concurrently by utilizing stochastic prior information for the estimation of model coefficients in replicated ultrastructural measurement error (RUME) models. To this end, three classes of stochastic restricted estimators and their feasible forms are proposed. Large sample properties of newly introduced estimators are studied without making any distributional assumption. To evaluate the performance of newly defined estimators a numerical example is done by using real data, Cigar data set, and a Monte Carlo simulation study is also conducted. It is concluded that the newly proposed stochastic restricted estimators outperform the predefined estimators for the RUME models in the existence of multicollinearity.