Strong consistency of regression function estimator with martingale difference errors

In this paper, we consider the regression model with fixed design: Yi=g(xi)+εi{Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i}, 1≤i≤n1\le i\le n, where {xi}\left\{{x}_{i}\right\} are the nonrandom design points, and {εi}\left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and gg is an unknown fu...

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Autor principal:	Chen Yingxia
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	regression function martingale difference consistency 60f15 62g05 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/14377688ba5a45968b770d487b495447
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spelling	oai:doaj.org-article:14377688ba5a45968b770d487b4954472021-12-05T14:10:53ZStrong consistency of regression function estimator with martingale difference errors2391-545510.1515/math-2021-0090https://doaj.org/article/14377688ba5a45968b770d487b4954472021-09-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0090https://doaj.org/toc/2391-5455In this paper, we consider the regression model with fixed design: Yi=g(xi)+εi{Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i}, 1≤i≤n1\le i\le n, where {xi}\left\{{x}_{i}\right\} are the nonrandom design points, and {εi}\left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and gg is an unknown function. Nonparametric estimator gn(x){g}_{n}\left(x) of g(x)g\left(x) will be introduced and its strong convergence properties are established.Chen YingxiaDe Gruyterarticleregression functionmartingale differenceconsistency60f1562g05MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 1056-1068 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	regression function martingale difference consistency 60f15 62g05 Mathematics QA1-939
spellingShingle	regression function martingale difference consistency 60f15 62g05 Mathematics QA1-939 Chen Yingxia Strong consistency of regression function estimator with martingale difference errors
description	In this paper, we consider the regression model with fixed design: Yi=g(xi)+εi{Y}_{i}=g\left({x}_{i})+{\varepsilon }_{i}, 1≤i≤n1\le i\le n, where {xi}\left\{{x}_{i}\right\} are the nonrandom design points, and {εi}\left\{{\varepsilon }_{i}\right\} is a sequence of martingale, and gg is an unknown function. Nonparametric estimator gn(x){g}_{n}\left(x) of g(x)g\left(x) will be introduced and its strong convergence properties are established.
format	article
author	Chen Yingxia
author_facet	Chen Yingxia
author_sort	Chen Yingxia
title	Strong consistency of regression function estimator with martingale difference errors
title_short	Strong consistency of regression function estimator with martingale difference errors
title_full	Strong consistency of regression function estimator with martingale difference errors
title_fullStr	Strong consistency of regression function estimator with martingale difference errors
title_full_unstemmed	Strong consistency of regression function estimator with martingale difference errors
title_sort	strong consistency of regression function estimator with martingale difference errors
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/14377688ba5a45968b770d487b495447
work_keys_str_mv	AT chenyingxia strongconsistencyofregressionfunctionestimatorwithmartingaledifferenceerrors
_version_	1718371585043202048

Strong consistency of regression function estimator with martingale difference errors

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