Research output: Contribution to journal › Article › peer-review
Universal weighted kernel-type estimators for some class of regression models. / Borisov, Igor S.; Linke, Yuliana Yu; Ruzankin, Pavel S.
In: Metrika, Vol. 84, No. 2, 02.2021, p. 141-166.Research output: Contribution to journal › Article › peer-review
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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.
N1 - Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.
PY - 2021/2
Y1 - 2021/2
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
VL - 84
SP - 141
EP - 166
JO - Metrika
JF - Metrika
SN - 0026-1335
IS - 2
ER -
ID: 23801924