Robust methods for model order estimation

Abstract

Model order estimation is a subject in time series analysis that deals with fitting a parametric model to a vector of observations. This paper focuses on several model order estimators known in the literature and examines their performance under small deviations of the probability distribution of the noise with respect to a nominal distribution assumed in the model. It is demonstrated that the standard estimators suffer from high sensitivity to deviations from the nominal distribution, and a drastic performance degradation is experienced. To overcome this problem, robust estimators that are insensitive to small deviations from the nominal distribution are developed. These estimators are based on a composition between model order estimation methods and robust statistical inference techniques known in the literature. In addition, a new estimator based on a locally best test for weak signals is presented both in nonrobust and robust versions. The proposed robust model order estimators are developed on a heuristic basis, and there is no claim of optimality, but experimental results indicate that they provide significant improvement over the standard estimators.