Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes

Echarif Elharfaoui; Michel Harel

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Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes

机译：渐进平稳绝对正则随机过程的光滑经验分布函数的中心极限定理

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Let F^n be an estimator obtained by integrating a kernel type density estimator based on a random sample of size n. A central limit theorem is established for the target statistic F^n(ξ^n), where the underlying random vector forms an asymptotically stationary absolutely regular stochastic process, and ξ^n is an estimator of a multivariate parameter ξ by using a vector of U-statistics. The results obtained extend or generalize previous results from the stationary univariate case to the asymptotically stationary multivariate case. An example of asymptotically stationary absolutely regular multivariate ARMA process and an example of a useful estimation of F(ξ) are given in the applications.

机译：令F n是通过基于大小为n的随机样本对核类型密度估计器进行积分而获得的估计器。为目标统计量F ^ n（ξ^ n）建立一个中心极限定理，其中基础随机向量形成一个渐近平稳的绝对正则随机过程，而ξ^ n是一个向量为的多元参数ξ的估计U统计量。获得的结果将先前的结果从平稳单变量情况扩展或推广到渐近平稳多元情况。在应用中给出了一个渐近平稳的绝对正则多元ARMA过程的示例以及一个有用的F（ξ）估计示例。

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《Journal of applied mathematics and stochastic analysis: J.A.M.S.A》 |2008年第1期|共18页
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Echarif Elharfaoui; Michel Harel;
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正文语种 eng
中图分类应用数学;
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1. Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes [J] . Echarif Elharfaoui, Michel Harel Journal of applied mathematics and stochastic analysis: J.A.M.S.A . 2008,第1期

机译：渐进平稳绝对正则随机过程的光滑经验分布函数的中心极限定理
2. Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes [J] . Echarif Elharfaoui, Michel Harel Journal of applied mathematics and stochastic analysis: J.A.M.S.A . 2008,第1期

机译：渐进平稳绝对正则随机过程的光滑经验分布函数的中心极限定理
3. Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes [J] . EcharifElharfaoui, MichelHarel International journal of stochastic analysis . 2008,第1期

机译：渐进平稳绝对正则随机过程的光滑经验分布函数的中心极限定理
4. Stationary Processes and Limit Theorems With Upper Semi-Continuous Function Values [C] . Li Guan, Shoumei Li The 10th International Conference on Intelligent Technologies(第十届智慧科技国际会议 InTech'09) . 2009

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5. ERGODICITY AND FUNCTIONAL CENTRAL LIMIT THEOREMS FOR A CLASS OF MARKOV PROCESSES WITH APPLICATIONS TO NONLINEAR AUTOREGRESSIVE MODELS (INVARIANT, PROBABILITY). [D] . LEE, OESOOK. 1986

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7. Almost sure central limit theorems for functionals of absolutely regular processes with application to U-statistics [O] . Chen Shouquan, Lin Zhengyan 2008

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8. Central Limit Theorems for Empirical and U-Processes of Stationary MixingSequences [R] . Arcones, M. A., Yu, B. 1994

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Central Limit Theorem of the Smoothed Empirical Distribution Functions for Asymptotically Stationary Absolutely Regular Stochastic Processes

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