Robust estimation ofk-component univariate normal mixtures |
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Authors: | B R Clarke C R Heathcote |
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Institution: | (1) School of Mathematical and Physical Sciences, Murdoch University, 6150, Western Australia, Australia;(2) Department of Statistics, Australian National University, GPO Box 4, 2601 Canberra ACT, Australia |
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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 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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Keywords: | Influence function weak continuity mixtures of normals Fré cht differentiability consistency asymptotic normality selection functional minimum distance estimator |
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