Gontar O. Asymptotic behavior of Simex-estimator in errors-in-variables regression models

Linear, polynomial, and general nonlinear regression models are considered. It is shown that with some extrapolation function, Simex-estimator in linear models is consistent and asymptotically equivalent to the Total Least Squares estimator in case of uknown measurement error variance. Asymptotic normality of Simex-estimator in linear errors-in-variables model is proved and explicit form of asymptotical covariance matrix is obtained. The consistency of Simex-estimator in case of certain extrapolation function for polynomial errors-in-variables regression model is shown. The modification of Simex-estimator for small samples is proposed. This modification has good numerical perfomance for small samples and preserves asymptotic properties of unmodified estimator. The asymptotic behavior of Simex-estimator in general nonlinear errors-in-variables regression models is considered. It is shown that asymptotic deviation of Simex-estimator is negligible compared to the measurement error variance, meanwhile theasymptotical deviation of naive estimator is proportional to the variance. Similar results are obtained for the misclassification problem