论文标题
使用样品矩进行密度估算的非经典参数化
A Non-Classical Parameterization for Density Estimation Using Sample Moments
论文作者
论文摘要
概率密度估计是统计和信号处理的核心问题。力矩方法是密度估计的重要手段，但是它们通常很大程度上取决于可行功能的选择，这严重影响了性能。在本文中，我们提出了一个非经典参数化，以使用样品矩进行密度估计，这不需要选择此类功能。参数化是由平方的hellinger距离诱导的，它的解决方案被证明存在，并且是独特的，以简单的先验为准，并不取决于数据，并且可以通过convex优化获得。密度估计器的统计特性以及渐近误差上限是通过功率矩提出的。提出的密度估计器在信号处理任务中的应用。模拟结果通过与几种流行方法进行比较来验证估计器的性能。据我们所知，提出的估计器是文献中的第一个估计器，其功率矩达到任意订单甚至完全符合样本矩，而真实密度则不属于特定功能类别。
Probability density estimation is a core problem of statistics and signal processing. 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. In this paper, we propose a non-classical parametrization for density estimation using sample moments, which does not require the choice of such functions. The parametrization is induced by the squared Hellinger distance, and the solution of it, which is proved to exist and be unique subject to a simple prior that does not depend on data, and can be obtained by convex optimization. Statistical properties of the density estimator, together with an asymptotic error upper bound are proposed for the estimator by power moments. Applications of the proposed density estimator in signal processing tasks are given. Simulation results validate the performance of the estimator by a comparison to several prevailing methods. To the best of our knowledge, the proposed estimator is the first one in the literature for which the power moments up to an arbitrary even order exactly match the sample moments, while the true density is not assumed to fall within specific function classes.
