Derivation of influence functions on skewness and analysis of its role†
A La Jeh1 · Yun Hee Lee2 · Honggie Kim3
1Statistics Korea
23Department of Information and Statistics, Chungnam National University
23Department of Information and Statistics, Chungnam National University
Correspondence to: † This article is a condensed form of the first author’s doctoral thesis from Chungnam National University. This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government(NRF-2022M3J6A1084843).
1 Officer, Statistics Korea, Daejeon 35208, Korea.
2 Ph.D. assistant, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea.
3 Professor, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea. E-mail : honggiekim@cnu.ac.kr
1 Officer, Statistics Korea, Daejeon 35208, Korea.
2 Ph.D. assistant, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea.
3 Professor, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea. E-mail : honggiekim@cnu.ac.kr
Received April 24, 2024; Revised May 23, 2024; Accepted May 30, 2024.
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 this study, the influence function on skewness is derived by using the influence functions on the third central moment and the third power of the standard deviation. Based on the empirical distribution obtained from the sample, we examine the relationship between the actual difference in skewness, when excluding or adding one observation, and the estimated difference. In addition, in order to verify the validity of the influence function on skewness, a close computation is conducted using data with an asymmetric distribution obtained from the National Statistical Office survey data and the results are examined. This study is meaningful in that it examines the role and meaning of the influence function on skewness.
- Keywords : Actual difference, empirical influence function, estimated difference, influence function, outlier, skewness
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