Journal of Statistical Theory and Applications

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Volume 19, Issue 3, September 2020, Pages 460 - 471

Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation

Authors
Langat Reuben Cheruiyot*
Department of Mathematics and Computer Sciences, School of Science and Technology, University of Kabianga, Kericho, Kenya
Corresponding Author
Langat Reuben Cheruiyot
Received 15 June 2020, Accepted 13 October 2020, Available Online 23 October 2020.
DOI
10.2991/jsta.d.201016.001How to use a DOI?
Keywords
Kernel estimators; Nonparametric regression estimation; Local linear regression; Bias; Variance; Asymptotic mean integrated square error (AMISE)
Abstract

The precision and accuracy of any estimation can inform one whether to use or not to use the estimated values. It is the crux of the matter to many if not all statisticians. For this to be realized biases of the estimates are normally checked and eliminated or at least minimized. Even with this in mind getting a model that fits the data well can be a challenge. There are many situations where parametric estimation is disadvantageous because of the possible misspecification of the model. Under such circumstance, many researchers normally allow the data to suggest a model for itself in the technique that has become so popular in recent years called the nonparametric regression estimation. In this technique the use of kernel estimators is common. This paper explores the famous Nadaraya–Watson estimator and local linear regression estimator on the boundary bias. A global measure of error criterion-asymptotic mean integrated square error (AMISE) has been computed from simulated data at the empirical stage to assess the performance of the two estimators in regression estimation. This study shows that local linear regression estimator has a sterling performance over the standard Nadaraya–Watson estimator.

Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Journal
Journal of Statistical Theory and Applications
Volume-Issue
19 - 3
Pages
460 - 471
Publication Date
2020/10/23
ISSN (Online)
2214-1766
ISSN (Print)
1538-7887
DOI
10.2991/jsta.d.201016.001How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis Press B.V.
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Langat Reuben Cheruiyot
PY  - 2020
DA  - 2020/10/23
TI  - Local Linear Regression Estimator on the Boundary Correction in Nonparametric Regression Estimation
JO  - Journal of Statistical Theory and Applications
SP  - 460
EP  - 471
VL  - 19
IS  - 3
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.d.201016.001
DO  - 10.2991/jsta.d.201016.001
ID  - Cheruiyot2020
ER  -