Median robust nonlinear weighted total least squares estimator of nonlinear EIV models: three algorithms

Abstract

To improve robust estimation performance of fully correlated nonlinear error-in-variables model, three median robust estimate methods are discussed on base of Nonlinear Weighted Total Least Squares (NWTLS), namely, median parameter method, median parameter initial value method and median variance method. After the discussion of the median robust estimation theory and the derivation of the calculation formula of the three median robust estimation methods, three iterative algorithms are developed. Through two nonlinear regression examples, four schemes including no artificial outliers, different location of outliers, different degrees of correlation, and different ratios of outliers are adopted, which proves the feasibility and effectiveness of the proposed algorithm. The experimental results show that from the statistical point of view, although the three median methods have different antioutlier effects for different nonlinear models, they are more effective than RNWTLS and NWTLS; the robust estimation results of three median methods are related to the functional model.