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arXiv 1704.04536stat.ME
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基于小波经验过程的发散度估计及其渐近正态性理论

Divergence Measures Estimation and Its Asymptotic Normality Theory Using Wavelets Empirical Processes

Gane Samb Lo, Amadou Diadié Ba, Diam Ba

摘要:

本文给出了广义$ϕ$ -发散测度的渐近理论,其中包括最常见的发散测度:Renyi族和Tsallis族以及Kullback-Leibler测度.而不是使用Parzen非参数估计的概率密度函数的差异估计,我们使用小波的方法和几何的Besov空间。单侧和双侧统计检验以及对称化估计。在一般情况下得到了几乎处处收敛速度和渐近正态性定理,并对Renyi族和Tsallis族以及Kullback-Leibler测度进行了特殊化.结果的适用性通常的分布函数的地址。

英文摘要:

In this paper we provide the asymptotic theory of the general of $ϕ$-divergences measures, which includes the most common divergence measures : Renyi and Tsallis families and the Kullback-Leibler measure. Instead of using the Parzen nonparametric estimators of the probability density functions whose discrepancy is estimated, we use the wavelets approach and the geometry of Besov spaces. One-sided and two-sided statistical tests are derived as well as symmetrized estimators. Almost sure rates of convergence and asymptotic normality theorem are obtained in the general case, and next particularized for the Renyi and Tsallis families and for the Kullback-Leibler measure as well. The applicability of the results to usual distribution functions is addressed.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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