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.
Unable to display preview. Download preview PDF.
- Donoho, D. L. and Liu, R. C. (1987). Geometrizing rates of convergence, I. Technical Report, Dept. Statist., Univ. California, Berkeley.Google Scholar
- Fan, J. (1991c). Adaptively local 1-dimensional subproblems. Preprint.Google Scholar
- Shohat, J. and Tamarkin, J. (1943). The Problem of Moments. Amer. Math. Soc. Waverly Press, Baltimore.Google Scholar