Abstract
The estimating equations derived from minimising aL 2 distance between the empirical distribution function and the parametric distribution representing a mixture ofk normal distributions with possibly different means and/or different dispersion parameters are given explicitly. The equations are of theM estimator form in which the ψ 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.
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Clarke, B.R., Heathcote, C.R. Robust estimation ofk-component univariate normal mixtures. Ann Inst Stat Math 46, 83–93 (1994). https://doi.org/10.1007/BF00773595
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DOI: https://doi.org/10.1007/BF00773595