Robust estimation ofk-component univariate normal mixtures

Clarke, B.R. and Heathcote, C.R. (1994) Robust estimation ofk-component univariate normal mixtures. Annals of the Institute of Statistical Mathematics, 46 (1). pp. 83-93.

Abstract

The estimating equations derived from minimising a L2 distance between the empirical distribution function and the parametric distribution representing a mixture of k normal distributions with possibly different means and/or different dispersion parameters are given explicitly. The equations are of the M estimator form in which the psi function is smooth, bounded and has bounded partial derivatives. As a consequence it is shown that there is a solution of the equations which is robust. In particular there exists a weakly continuous, Fréchet differentiable root and hence there is a consistent root of the equations which is asymptotically normal. These estimating equations offer a robust alternative to the maximum likelihood equations, which are known to yield nonrobust estimators.