Adaptive Mixtures
Carey E. Priebe · Journal of the American Statistical Association · 1994
The estimation of a probability density function based on a sample of independent identically distributed observations is essential in a wide range of applications. In particular, a sequence of estimates that converges in some sense to the true density α 0 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 L 1 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.