Abstract: Consistent weighted least square estimators are proposed for a wide class of nonparametric regression models with random regression function, where this real-valued random function of k arguments is assumed to be continuous with probability 1. We obtain explicit upper bounds for the rate of uniform convergence in probability of the new estimators to the unobservable random regression function for both fixed or random designs. In contrast to the predecessors' results, the bounds for the convergence are insensitive to the correlation structure of the k-variate design points. As an application, we study the problem of estimating the mean and covariance functions of random fields with additive noise under dense data conditions. The theoretical results of the study are illustrated by simulation examples which show that the new estimators are more accurate in some cases than the Nadaraya–Watson ones. An example of processing real data on earthquakes in Japan in 2012–2021 is included.

Cite: Linke Y.Y. , Borisov I.S. , Ruzankin P.S.
Universal kernel-type estimation of random fields
Statistics. 2023. V.57. N4. P.785-810. DOI: 10.1080/02331888.2023.2231114 WOS Scopus РИНЦ OpenAlex

Dates:

Submitted:	Oct 5, 2022
Accepted:	Jun 23, 2023
Published online:	Jul 10, 2023
Published print:	Aug 19, 2023

Identifiers:

Web of science:	WOS:001023087300001
Scopus:	2-s2.0-85164667208
Elibrary:	62401280
OpenAlex:	W4383175964

Citing:

DB	Citing
Scopus	5
Web of science	3
OpenAlex	5
Elibrary	4

Altmetrics: