Complete f -moment convergence for weighted sums of WOD arrays with statistical applications

Xi Chen; Xinran Tao; Xuejun Wang

Kybernetika (2023)

  • Volume: 59, Issue: 1, page 1-27
  • ISSN: 0023-5954

Abstract

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Complete f -moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete f -moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete f -moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.

How to cite

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Chen, Xi, Tao, Xinran, and Wang, Xuejun. "Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications." Kybernetika 59.1 (2023): 1-27. <http://eudml.org/doc/299075>.

@article{Chen2023,
abstract = {Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.},
author = {Chen, Xi, Tao, Xinran, Wang, Xuejun},
journal = {Kybernetika},
keywords = {widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency},
language = {eng},
number = {1},
pages = {1-27},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications},
url = {http://eudml.org/doc/299075},
volume = {59},
year = {2023},
}

TY - JOUR
AU - Chen, Xi
AU - Tao, Xinran
AU - Wang, Xuejun
TI - Complete $f$-moment convergence for weighted sums of WOD arrays with statistical applications
JO - Kybernetika
PY - 2023
PB - Institute of Information Theory and Automation AS CR
VL - 59
IS - 1
SP - 1
EP - 27
AB - Complete $f$-moment convergence is much more general than complete convergence and complete moment convergence. In this work, we mainly investigate the complete $f$-moment convergence for weighted sums of widely orthant dependent (WOD, for short) arrays. A general result on Complete $f$-moment convergence is obtained under some suitable conditions, which generalizes the corresponding one in the literature. As an application, we establish the complete consistency for the weighted linear estimator in nonparametric regression models. Finally, some simulations are provided to show the numerical performance of theoretical results based on finite samples.
LA - eng
KW - widely orthant dependent arrays; weighted sums; complete $f$-moment convergence; complete convergence; nonparametric regression models; complete consistency
UR - http://eudml.org/doc/299075
ER -

References

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