Consistent estimation approach to tackling collinearity and Berkson-type measurement error in linear regression using adjusted Wald-type estimator

This article proposes a consistent estimation approach in linear regression models for the case when the predictor variables are subject to collinearities and Berkson-type measurement errors simultaneously. Our presented procedure does not rely on ridge regression (RR) methods that have been widely addressed in the literature for ill-conditioned problems resulted from multicollinearity. Instead, we review and propose new consistent estimators due to Wald (1940 Wald, A. (1940). Fitting of straight lines if both variables are subject to error. Ann. Math. Stat. 11:284–300.[Crossref] , [Google Scholar]) so that, except finite fourth moments assumptions, no prior knowledge of parametric settings on observations and errors is used, and there is no need to solve estimating equations for coefficient parameters. The performance of the estimation procedure is compared with that of RR-based estimators by using a variety of numerical experiments through Monte Carlo simulation under estimated mean squared error (EMSE) criterion.