Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response
Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response
Local linear kernel fitting is a popular nonparametric technique for modelling nonlinear time series data. Investigations into it, although extensively made for continuousvalued case, are still rare for the time series that are discrete-valued. In this paper, we propose and develop the uniform consistency of local linear maximum likelihood (LLML) fitting for time series regression allowing response to be discrete-valued under β-mixing dependence condition. Specifically, the uniform consistency of LLML estimators is established under time series conditional exponential family distributions with aid of a beta-mixing empirical process through local estimating equations. The rate of convergence is also provided under mild conditions. Performances of the proposed method are demonstrated by a Monte-Carlo simulation study and an application to COVID-19 data.
Uniform consistency, Discrete-valued time series, Exponential family, Local linear fitting, beta-mixing, Non-parametric, β-mixing, Non-parametric, Discretevalued time series, Local linear fitting, Exponential family, Uniform consistency
305 – 318
Peng, Rong
a82d230a-2ab9-4b41-993a-cd5eb21b41a7
Lu, Zudi
4aa7d988-ac2b-4150-a586-ca92b8adda95
2023
Peng, Rong
a82d230a-2ab9-4b41-993a-cd5eb21b41a7
Lu, Zudi
4aa7d988-ac2b-4150-a586-ca92b8adda95
Peng, Rong and Lu, Zudi
(2023)
Uniform consistency for local fitting of time series non-parametric regression allowing for discrete-valued response.
Statistics and Its Interface, 16 (2), .
(doi:10.4310/22-SII745).
Abstract
Local linear kernel fitting is a popular nonparametric technique for modelling nonlinear time series data. Investigations into it, although extensively made for continuousvalued case, are still rare for the time series that are discrete-valued. In this paper, we propose and develop the uniform consistency of local linear maximum likelihood (LLML) fitting for time series regression allowing response to be discrete-valued under β-mixing dependence condition. Specifically, the uniform consistency of LLML estimators is established under time series conditional exponential family distributions with aid of a beta-mixing empirical process through local estimating equations. The rate of convergence is also provided under mild conditions. Performances of the proposed method are demonstrated by a Monte-Carlo simulation study and an application to COVID-19 data.
Text
SII745-proof
- Accepted Manuscript
More information
Accepted/In Press date: 13 June 2022
e-pub ahead of print date: 13 April 2023
Published date: 2023
Additional Information:
Funding Information:
The authors are grateful to the Editor-in-Chief, Professor Ming-Hui Chen, and an Associate Editor, a Co Guest-Editor and two referees for their valuable and constructive comments and suggestions, which have greatly helped to improve the presentation of this paper. The research was partially supported by British Academy/Leverhulme Trust (No.SG162909) and NSFC (No.71971131), which are acknowledged.
Publisher Copyright:
© 2022 American Psychological Association
Keywords:
Uniform consistency, Discrete-valued time series, Exponential family, Local linear fitting, beta-mixing, Non-parametric, β-mixing, Non-parametric, Discretevalued time series, Local linear fitting, Exponential family, Uniform consistency
Identifiers
Local EPrints ID: 468367
URI: http://eprints.soton.ac.uk/id/eprint/468367
ISSN: 1938-7989
PURE UUID: 67f4cc20-2e19-486c-ba64-3042ce071052
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Date deposited: 11 Aug 2022 16:43
Last modified: 17 Mar 2024 07:25
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Author:
Rong Peng
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