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.