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Improved orthogonal polynomial density estimates

机译：改进的正交多项式密度估计

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摘要

Density estimates that are expressible as the product of a base density function and a linear combination of orthogonal polynomials are considered in this paper. More specifically, two criteria are proposed for determining the number of terms to be included in the polynomial adjustment component and guidelines are suggested for the selection of a suitable base density function. A simulation study reveals that these stopping rules produce density estimates that are generally more accurate than kernel density estimates or those resulting from the application of the Kronmal-Tarter criterion. Additionally, it is explained that the same approach can be utilized to obtain multivariate density estimates. The proposed orthogonal polynomial density estimation methodology is applied to several univariate and bivariate data sets, some of which have served as benchmarks in the statistical literature on density estimation.
机译：本文考虑了可表达为基本密度函数和正交多项式线性组合的乘积的密度估计。更具体地，提出了两个标准来确定要包括在多项式调整分量中的项的数量，并且提出了用于选择合适的基本密度函数的准则。仿真研究表明，这些停止规则产生的密度估计值通常比内核密度估计值或使用Kronmal-Tarter准则得出的结果更准确。另外，解释了可以利用相同的方法来获得多元密度估计。提出的正交多项式密度估计方法适用于几个单变量和双变量数据集，其中一些已作为密度估计的统计文献中的基准。

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