Using Wald-type estimator to combat outliers and Berkson-type uncertainties with mixture distributions in linear regression models

The impacts of outliers and Berkson-type uncertainties with additive and multiplicative errors in linear regression are investigated. The work is motivated by a common biological phenomenon in which outlying observations and Berkson-type uncertainties may lie partly in the data, causing incorrect estimations and inferences. In this article, we use Wald-type estimator to combat these uncertainties due to its merits, including large sample properties especially for asymmetric errors, as well as its simplicity without nuisance parameters. The severity of the neglect of uncertainty effects will be examined by Monte Carlo simulations and real data examples through comparison with residual-based methods and the proposed estimate.