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Estimation of second moment function with adujusted sample by an estimator of jump size of discontinuity point
Journal of the Korean Data & Information Science Society 2021;32:757-66
Published online July 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.4.757
© 2021 Korean Data and Information Science Society.

Jib Huh1

1Department of Statistics, Duksung Women’s University
Correspondence to: 1 Professor, Department of Statistics, Duksung Women’s University, Seoul 01369, Korea.
E-mail: jhuh@duksung.ac.kr
Received June 11, 2021; Revised June 18, 2021; Accepted July 1, 2021.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
In the case that the regression function is continuous, the discontinuity of the variance function comes from the discontinuous second moment function. In this paper, the estimator of second moment function is proposed by a kernel type estimator using the adjusted squared observations of response variable by an estimator of jump size of the second moment function. After that, the final estimator of the discontinuous second moment function is proposed by reverse adjustment of the kernel type estimator of the second moment function using an estimator of jump size. The estimated second moment function based on the data sets divided by an estimated location has the boundary problem around the location of the discontinuity point like any other kernel type estimators of the statistical functions do. However, the proposed estimator of second moment function does not have the boundary problem near the discontinuity point. Simulation and analysis of real data set demonstrate the performances of the estimators of second moment function.
Keywords : Discontinuity point, LIDAR, Nadaraya-Watson estimator, variance function.