ADAPTIVE MIXTURES

The estimation of a probability density function based on a sample {ze ta(i)}(n)(i=1) of independent identically distributed observations is essential in a wide range of applications. In particular, a sequence o f estimates <(alpha)over cap>(n) that converges in some sense to the t rue density alpha(0) can yield asymptotically optimal performance in c lassification and discrimination problems. In this article an estimati on technique called ''adaptive mixtures'' is developed from the relate d methods of kernel estimation and finite mixture models. Asymptotic p roperties of adaptive mixtures are obtained via the so-called method o f sieves, yielding almost sure L(1) convergence. Monte Carlo simulatio ns indicate the performance of the method, and an experimental study b ased on a typical discrimination problem is performed, indicating the scope of applicability.