Abstract
Let X 1, X 2, ..., X n be independent and identically distributed observations from a mixture of power series distributions. Based on this random sample, we consider the problem of estimating the mixing density of the mixture distribution. A mixing density kernel estimator is proposed which, under mild assumptions, has 1/log n as an upper bound for its rate of convergence to the true density under squared error loss. It is also shown that the optimal rate of convergence cannot exceed 1/n r for any constant r.
Research supported in part by NSF Grant DMS 89-23071.
I would like to thank Professors Herman Rubin and Bill Studden for kindling my interest in mixture problems, which eventually resulted in this work.
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© 1994 Springer-Verlag New York, Inc.
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Loh, WL. (1994). Estimating the Mixing Density of a Mixture of Power Series Distributions. In: Gupta, S.S., Berger, J.O. (eds) Statistical Decision Theory and Related Topics V. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2618-5_7
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DOI: https://doi.org/10.1007/978-1-4612-2618-5_7
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