CONVERGENCE OF NON-LINEAR FUNCTIONALS OF SMOOTHED EMPIRICAL PROCESSES AND KERNEL DENSITY ESTIMATES

CORINNE BERZIN; JOSE R. LEON; JOAQUIN ORTEGA

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CONVERGENCE OF NON-LINEAR FUNCTIONALS OF SMOOTHED EMPIRICAL PROCESSES AND KERNEL DENSITY ESTIMATES

机译：平稳经验过程和核密度估计的非线性函数的收敛性

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摘要

We consider regularizations by convolution of the empirical process and study the asymptotic behaviour of nonlinear functionals of this process. Using a result for the same type of non-linear functionals of the Brownian bridge, shown in a previous paper, and a strong approximation theorem, we prove several results for the p-deviation in estimation of the derivatives of the density. We also study the asymptotic behaviour of the number of crossings of the smoothed empirical process defined by Yukich and of a modified version of the Kullback deviation.

机译：我们通过经验过程的卷积考虑正则化，并研究此过程的非线性泛函的渐近行为。使用先前论文中所示的布朗桥的相同类型的非线性泛函的结果以及强逼近定理，我们证明了p偏差估算密度导数时的几种结果。我们还研究了Yukich定义的平滑经验过程的交叉次数和Kullback偏差的修改版本的渐近行为。

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来源
《Statistics》 |2003年第3期|p.217-242|共26页
作者
CORINNE BERZIN; JOSE R. LEON; JOAQUIN ORTEGA;
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作者单位

Universite Pierre Mendes-France, Grenoble, France;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类应用数学;
关键词
non-linear functionals; empirical process; kernel density estimation; crossings; kullback-leibler deviation; regularization by convolution;

机译：非线性泛函;经验过程;核密度估计;交叉;kullback-leibler偏差;通过卷积进行正则化;

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2. Moderate deviations of empirical periodogram and non-linear functionals of moving average processes [J] . H. Djellout, A. Guillin, L. Wu Annales de l'Institut Henri Poincare. Probabilites et Statistiques . 2006,第4期

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3. Estimating Mixture of Gaussian Processes by Kernel Smoothing [J] . Mian Huang, Runze Li, Hansheng Wang, Journal of business & economic statistics . 2014,第2期

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4. Smooth Kernel Density Estimate for Multiple View Reconstruction [C] . Ruttle J., Manzke M., Dahyot R. 7th Conference on Visual Media Production . 2010

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5. Adaptive Smoothing Parameter in Kernel Density Estimation and Parameter Estimation in Normal Mixture Distributions [D] . Mahzabeen, Sabiha. 2019

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6. Estimating Mixture of Gaussian Processes by Kernel Smoothing [O] . Mian Huang, Runze Li, Hansheng Wang, -1

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7. Moderate deviations for non-linear functionals and empirical spectral density of moving average processes [O] . Djellout, Hacene, Guillin, Arnaud, Wu, Liming 2004

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8. On the Pointwise and the Integral Convergence of Recursive Kernel Estimates of Probability Densities [R] . Devroye, L. P. 1977

机译：关于概率密度递归核估计的逐点收敛性和积分收敛性

CONVERGENCE OF NON-LINEAR FUNCTIONALS OF SMOOTHED EMPIRICAL PROCESSES AND KERNEL DENSITY ESTIMATES

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