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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 45, Fasc. 2,
pages 227 - 245
DOI: 10.37190/0208-4147.00270
Published online 27.2.2026
 

A new probability-type inequality for partial sums of widely orthant dependent random variables and its application to non-parametric regression models

O. E. Cherifi
K. Abdelhak
S. Benaissa
B. Mechab

Abstract:

This paper establishes an exponential inequality for a sequence of widely orthant dependent (WOD) random variables. Leveraging this result, we prove the strong consistency of a non-parametric regression estimator under a general moment condition. We further derive the convergence rate of this estimator, highlighting its alignment with classical results under specific parameter choices. As an application, we examine the nearest neighbor estimator and support our theoretical findings with a numerical study.

2010 AMS Mathematics Subject Classification: Primary 60E15; Secondary 60F15, 62G08.

Keywords and phrases: widely orthant dependence, probability inequality, non-parametric regression, strong consistency, convergence rate.

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