Asymptotic results for the regression function estimate on continuous time stationary and ergodic data

IF 1.3 Q2 STATISTICS & PROBABILITY

Statistics & Risk Modeling Pub Date : 2014-01-28 DOI:10.1515/strm-2012-1134

S. Didi, D. Louani

引用次数: 11

Abstract

Abstract This paper is devoted to the study of asymptotic properties of the regression function kernel estimate in the setting of continuous time stationary and ergodic data. More precisely, considering the Nadaraya–Watson type estimator, say m̂T(x), of the l-indexed regression function m(x) =𝔼 (l(Y)|X = x) built upon continuous time stationary and ergodic data (Xt, Yt)0≤t≤T, we establish its pointwise and uniform, over a dilative compact set, convergences with rates. Notice that the ergodic setting covers and completes various situations as compared to the mixing case and stands as more convenient to use in practice.

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连续时间平稳和遍历数据上回归函数估计的渐近结果

摘要本文研究了连续时间平稳遍历数据下回归函数核估计的渐近性质。更准确地说，考虑到建立在连续时间平稳和遍历数据(Xt, Yt)0≤T≤T上的l-索引回归函数m(x) = (l(Y)| x = x)的nadarya - watson型估计量m³T(x)，我们建立了它在一个扩张性紧集上的点性和均匀性，具有速率收敛性。请注意，与混合箱相比，遍历式设置涵盖并完成了各种情况，并且在实践中更方便使用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics & Risk Modeling STATISTICS & PROBABILITY-

CiteScore

1.80

自引率

6.70%

发文量

期刊介绍： Statistics & Risk Modeling (STRM) aims at covering modern methods of statistics and probabilistic modeling, and their applications to risk management in finance, insurance and related areas. The journal also welcomes articles related to nonparametric statistical methods and stochastic processes. Papers on innovative applications of statistical modeling and inference in risk management are also encouraged. Topics Statistical analysis for models in finance and insurance Credit-, market- and operational risk models Models for systemic risk Risk management Nonparametric statistical inference Statistical analysis of stochastic processes Stochastics in finance and insurance Decision making under uncertainty.