基于窗宽优化的鲁棒核密度估计器

A Robust Kernel Density Estimator Based on Window Width Optimization

摘要

核密度估计器作为一种非参数估计统计模型,在对数据进行概率密度函数估计时,其结果易受到异常点和窗口参数选择的影响.为了提升核密度在异常点条件下的估计准确性,提出了一种基于窗宽优化的鲁棒核密度估计器.该优化的估计器基于两个阶段来实现.在第一阶段中,首先通过引入莱维飞行策略来实现杂交水稻优化算法的寻优性能提升.该改进的杂交水稻优化算法将被用于优化无偏交叉验证目标函数,实现搜索最优的窗口值.在第二阶段中,将M稳健估计引入希尔伯特空间映射后的均值计算过程,降低了异常点在概率密度函数计算过程中的权重,排除异常点的影响.通过上述两个阶段的优化,最终达成异常点条件下概率密度函数的精准估计目标.实验结果表明,当数据中包含有异常值时,优化后的鲁棒核密度估计器比传统的核密度估计器具有更高的估计准确性.

Abstract

The kernel density estimator, as a non-parametric estimation statistical model, is susceptible to the influence of outlier and window parameter selection when estimating the probability density function of data. In order to improve the accuracy of kernel density estimation under outlier conditions, this study proposes a robust kernel density estimator based on window width optimization. The optimized estimator is implemented in two stages. In the first stage, this study introduces the Levi flight strategy to improve the optimization performance of hybrid rice optimization algorithms. The improved hybrid rice optimization algorithm will be used to optimize the unbiased cross validation objective function and achieve the search for the optimal window value. In the second stage, this study introduces M-robust estimation into the mean calculation process of Hilbert space mapping, reducing the weight of outliers in the probability density function calculation process and eliminating the influence of outliers. Through the optimization of the above two stages, the goal of accurately estimating the probability density function under outlier conditions is ultimately achieved. The experimental results show that when the data contains outliers, the optimized robust kernel density estimator has higher estimation accuracy than traditional kernel density estimators.

关键词

稳健估计 / 鲁棒核密度估计 / 杂交水稻优化算法 / 莱维飞行 / 希尔伯特空间

Key words

robust estimation / kernel density estimation / hybrid rice optimization algorithm / Lévy fight / Hibert space

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