Adaptive Mixtures
提出一种结合核估计与有限混合模型的自适应混合密度估计方法，证明其几乎必然L1收敛，并通过蒙特卡洛模拟和判别实验展示其性能。
Abstract 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.