Robust estimation in the multivariate normal model with variance components

Abstract

Fisher consistent and Fréchet differentiable statistical functionals have been already used by Bednarski and Zontek [Robust estimation of parameters in a mixed unbalanced model. Ann Statist. 1996;24(4):1493–1510] to get a robust estimator of parameters in a two-way crossed classification mixed model. This way of robust estimation appears also in the variance components model with a commutative covariance matrix [Zmyślony, Zontek. Robust M-estimator of parameters in variance components model. Discuss Math Probab Stat. 2002;22:61–71]. In this paper it is shown that a modification of this method does not involve any assumptions about commutation of covariance matrix. The theoretical results have been completed with computer simulation studies. Robustness of considered estimator and possibility of approximation of the estimator's distribution with some multivariate normal distribution for both model and contaminated data have been confirmed there.

Keywords:

• asymptotic normality
• Fisher consistency
• Fréchet differentiability
• multivariate robust estimation
• statistical functional

MSC 2010:

• 62H10
• 62H12