Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2020; 57(1): 51-68

Online first article December 4, 2019      Printed January 31, 2020

https://doi.org/10.4134/BKMS.b181275

Copyright © The Korean Mathematical Society.

Almost sure and complete consistency of the estimator in nonparametric regression model for negatively orthant dependent random variables

Liwang Ding

Guangxi University of Finance and Economics

Abstract

In this paper, the author considers the nonparametric regression model with negatively orthant dependent random variables. The wavelet procedures are developed to estimate the regression function. For the wavelet estimator of unknown function $g(\cdot)$, the almost sure consistency is derived and the complete consistency is established under the mild conditions. Our results generalize and improve some known ones for independent random variables and dependent random variables.

Keywords: Negatively orthant dependent random variables, wavelet estimator, almost sure consistency, complete consistency

MSC numbers: 60E05, 60F15, 62G05

Supported by: This research is supported by the National Science Foundation of China (11271189), Science Foundation of Guangxi Education Department (2019KY0646), 2019 Youth Teacher Research and Development Fund Project of Guangxi University of Finance and Economics (2019QNB07), Discipline Project of School of Information and Statistics of Guangxi University of Finance and Economics (2019XTZZ07).