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Estimation of the number of discontinuity points in the variance function of LIDAR data
Journal of the Korean Data & Information Science Society 2021;32:37-47
Published online January 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.1.37
© 2021 Korean Data and Information Science Society.

Jib Huh1

1Department of Statistics, DuksungWomen’s University, Seoul 01369, Korea
Correspondence to: 1(01369) Professor, Department of Statistics, Duksung Women’s University, Seoul 01369, Korea. E-mail: jhuh@duksung.ac.kr

This research was supported by the Duksung Women’s University Research Grants 2019.
Received December 21, 2020; Revised January 15, 2021; Accepted January 15, 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
We can guess that there exist one or two discontinuity points in the variance function of LIDAR data in Ruppert et al. (1997). Kang and Huh (2006) proposed the Nadaraya-Watson estimators for the location and corresponding jump size of the variance function in regression model. To use some merits of the local polynomial estimator, Huh (2016) estimated the location and jump size of discontinuity point of log-variance function based on likelihood function. They suggested the testing for the existence of a discontinuity point with the asymptotic distribution of the estimator of the jump size. In this paper, algorithms of detection of the number of discontinuity points in the variance and log-variance function are introduced and illustrated by simulated example and LIDAR data.
Keywords : Discontinuity point, LIDAR, local linear estimator, log-variance function, Nadaraya-Watson estimator, variance function.