Estimating the Mixing Density of a Mixture of Power Series Distributions
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.
KeywordsOptimal Rate Mixture Distribution Error Loss Deconvolution Problem Compound Poisson Distribution
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