Universal Local Linear Kernel Estimators in Nonparametric Regression

Yuliana Linke, Igor Borisov, Pavel Ruzankin, Vladimir Kutsenko, Elena Yarovaya and Svetlana Shalnova
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Yuliana Linke: Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
Igor Borisov: Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
Pavel Ruzankin: Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
Vladimir Kutsenko: Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
Elena Yarovaya: Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia
Svetlana Shalnova: Department of Epidemiology of Noncommunicable Diseases, National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia

Mathematics, 2022, vol. 10, issue 15, 1-28

Abstract: New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

Keywords: nonparametric regression; kernel estimator; local linear estimator; uniform consistency; fixed design; random design; dependent design elements; mean of dense functional data; epidemiological research (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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