Extended Glivenko–Cantelli theorem and L 1 strong consistency of innovation density estimator for time-varying semiparametric ARCH model

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Journal of Nonparametric Statistics Pub Date : 2022-12-05 DOI:10.1080/10485252.2022.2152813

Chen Zhong

引用次数: 1

Abstract

ABSTRACT This paper extends the classical Glivenko–Cantelli theorem for the empirical cumulative distribution function based on the innovations in the ARCH model with a slowly time-varying trend. In this semiparametric time-varying model, strong consistency for the innovation density estimator via kernel smoothing method is established, given that the trend and ARCH parameter estimators meet some mild conditions. Besides, the strong consistency for the Gaussian quasi maximum likelihood estimator (QMLE) in the time-varying ARCH parameter is established as well. Moreover, in terms of the existence of the trend in the data, two major nonparametric trend estimators, B-spline and kernel estimators, are shown to be appropriate for the strong consistency results.

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时变半参数ARCH模型创新密度估计的扩展Glivenko-Cantelli定理和L 1强相合性

本文基于具有慢时变趋势的ARCH模型的创新，对经典的经验累积分布函数Glivenko-Cantelli定理进行了推广。在该半参数时变模型中，在趋势估计量和ARCH参数估计量满足一定温和条件的情况下，通过核平滑方法建立了创新密度估计量的强相合性。此外，还建立了时变ARCH参数下高斯拟极大似然估计的强相合性。此外，就数据中趋势的存在性而言，两种主要的非参数趋势估计量，b样条和核估计量，被证明适合于强一致性结果。

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

Journal of Nonparametric Statistics 数学-统计学与概率论

CiteScore

1.50

自引率

8.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Journal of Nonparametric Statistics provides a medium for the publication of research and survey work in nonparametric statistics and related areas. The scope includes, but is not limited to the following topics: Nonparametric modeling, Nonparametric function estimation, Rank and other robust and distribution-free procedures, Resampling methods, Lack-of-fit testing, Multivariate analysis, Inference with high-dimensional data, Dimension reduction and variable selection, Methods for errors in variables, missing, censored, and other incomplete data structures, Inference of stochastic processes, Sample surveys, Time series analysis, Longitudinal and functional data analysis, Nonparametric Bayes methods and decision procedures, Semiparametric models and procedures, Statistical methods for imaging and tomography, Statistical inverse problems, Financial statistics and econometrics, Bioinformatics and comparative genomics, Statistical algorithms and machine learning. Both the theory and applications of nonparametric statistics are covered in the journal. Research applying nonparametric methods to medicine, engineering, technology, science and humanities is welcomed, provided the novelty and quality level are of the highest order. Authors are encouraged to submit supplementary technical arguments, computer code, data analysed in the paper or any additional information for online publication along with the published paper.