TY - JOUR

T1 - Universal weighted kernel-type estimators for some class of regression models

AU - Borisov, Igor S.

AU - Linke, Yuliana Yu

AU - Ruzankin, Pavel S.

PY - 2020/3/2

Y1 - 2020/3/2

N2 - For a wide class of nonparametric regression models with random design, we suggest consistent weighted least square estimators, asymptotic properties of which do not depend on correlation of the design points. In contrast to the predecessors’ results, the design is not required to be fixed or to consist of independent or weakly dependent random variables under the classical stationarity or ergodicity conditions; the only requirement being that the maximal spacing statistic of the design tends to zero almost surely (a.s.). Explicit upper bounds are obtained for the rate of uniform convergence in probability of these estimators to an unknown estimated random function which is assumed to lie in a Hölder space a.s. A Wiener process is considered as an example of such a random regression function. In the case of i.i.d. design points, we compare our estimators with the Nadaraya–Watson ones.

AB - For a wide class of nonparametric regression models with random design, we suggest consistent weighted least square estimators, asymptotic properties of which do not depend on correlation of the design points. In contrast to the predecessors’ results, the design is not required to be fixed or to consist of independent or weakly dependent random variables under the classical stationarity or ergodicity conditions; the only requirement being that the maximal spacing statistic of the design tends to zero almost surely (a.s.). Explicit upper bounds are obtained for the rate of uniform convergence in probability of these estimators to an unknown estimated random function which is assumed to lie in a Hölder space a.s. A Wiener process is considered as an example of such a random regression function. In the case of i.i.d. design points, we compare our estimators with the Nadaraya–Watson ones.

KW - Kernel-type estimator

KW - Nonparametric regression

KW - Uniform consistency

KW - NONPARAMETRIC REGRESSION

KW - UNIFORM-CONVERGENCE RATES

KW - VARIANCE

UR - http://www.scopus.com/inward/record.url?scp=85081536807&partnerID=8YFLogxK

U2 - 10.1007/s00184-020-00768-0

DO - 10.1007/s00184-020-00768-0

M3 - Article

AN - SCOPUS:85081536807

JO - Metrika

JF - Metrika

SN - 0026-1335

ER -