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Adaptive Mixtures

Carey E. Priebe
Journal of the American Statistical Association
Vol. 89, No. 427 (Sep., 1994), pp. 796-806
DOI: 10.2307/2290905
Stable URL: http://www.jstor.org/stable/2290905
Page Count: 11
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Adaptive Mixtures
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Abstract

The estimation of a probability density function based on a sample {ζi}ni = 1 of independent identically distributed observations is essential in a wide range of applications. In particular, a sequence of estimates α̂n that converges in some sense to the true density α0 can yield asymptotically optimal performance in classification and discrimination problems. In this article an estimation technique called "adaptive mixtures" is developed from the related methods of kernel estimation and finite mixture models. Asymptotic properties of adaptive mixtures are obtained via the so-called method of sieves, yielding almost sure L1 convergence. Monte Carlo simulations indicate the performance of the method, and an experimental study based on a typical discrimination problem is performed, indicating the scope of applicability.

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