Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely affects the performance. We propose a non-classical parameterization for density estimation using the sample moments, which does not require the choice of such functions. The parameterization is induced by the Kullback-Leibler distance, and the solution of it, which is proved to exist and be unique subject to simple prior that does not depend on data, can be obtained by convex optimization. Simulation results show the performance of the proposed estimator in estimating multi-modal densities which are mixtures of different types of functions.
翻译:时间推移方法是密度估计的一个重要手段,但通常严重依赖选择可行的功能,这对性能有严重影响。我们提议使用抽样时间进行密度估计的非古典参数化,不需要选择这种功能。参数化是由Kullback-Lebeller距离引起的,其解决办法证明存在,并且是独特的,在不取决于数据的简单之前,不取决于数据,可以通过convex优化获得。模拟结果显示拟议的估计数字仪在估计不同类型功能混合的多模式密度方面的性能。