Robust estimators in mixed errors-in-variables models

Abstract

Traditional errors-in-variables (EIV) models are widely adopted in applied sciences. In practice, some of the columns of the coefficient matrix in EIV models may be known exactly. EIV models with exactly known columns are called mixed EIV (MEIV) models. Similar to EIV models, the MEIV models can be highly biased by gross error. This paper focuses on robust estimation in MEIV models. A new class of robust estimators, called robust weighted mixed total least squared (RWMTLS) estimators for the MEIV models by M-estimator and Lagrange multiplier method, is introduced. A simulated example is carried out to demonstrate the performance of the presented RWMTLS algorithm. The result shows that the RWMTLS algorithm can indeed resist gross error to achieve the reliable solution.