Abstract
A semiparametric method for estimating densities of normal mean mixtures is presented. This consistent data-driven method of estimation is based on probability spacings. The estimation technique involves iteratively fixing the standard deviation of the normal kernel that serves as a smoothing parameter, and then maximizing a function of the probability spacings over all mixing distributions. Based on the distribution of uniform spacings, a distribution free goodness-of-fit criterion is developed to guide the selection of the smoothing parameter. The result is a set of consistent estimators indexed by a range of smoothing parameters. Empirical process results are used to prove consistency.
Citation
Kathryn Roeder. "Semiparametric Estimation of Normal Mixture Densities." Ann. Statist. 20 (2) 929 - 943, June, 1992. https://doi.org/10.1214/aos/1176348664
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