Derivation of the influence function on the parameter σk and its application†
Yun Hee Lee1 · Mi Hong Yim2 · Mi Mi Ko3 · Honggie Kim4
14Department of Information and Statistics, Chungnam National University
23Korea Institute of Oriental Medicine
23Korea Institute of Oriental Medicine
Correspondence to: † This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2022M3J6A1084843).
1 Assistant, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea.
2 Technical resercher, Digital Health Research Division, Korea Institute of Oriental Medicine, Daejeon 34054, Korea.
3 Technical resercher, KM Science Research Division, Korea Institute of Oriental Medicine, Daejeon 34054, Korea.
4 Professor, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea. E-mail: honggiekim@cnu.ac.kr
1 Assistant, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea.
2 Technical resercher, Digital Health Research Division, Korea Institute of Oriental Medicine, Daejeon 34054, Korea.
3 Technical resercher, KM Science Research Division, Korea Institute of Oriental Medicine, Daejeon 34054, Korea.
4 Professor, Department of Information and Statistics, Chungnam National University, Daejeon 34134, Korea. E-mail: honggiekim@cnu.ac.kr
Received November 24, 2023; Revised December 21, 2023; Accepted December 25, 2023.
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 all statistical analyses, a presence of outlying observations lead us to a misunderstanding and bring us to a false decision. For these reasons, we can not overemphasize the importance of detecting and handling those outliers. There are several ways to study outliers including influence function, which provides a key to discriminate outlying observations from the most of usual ones. The influence function technique is first suggested by Hampel, then is applied in many statistical problems and is proved to be very effective to declrare outliers. In this paper, we use the influence function on σ2 to derive that on σk, and verify its validity using a real data set. It is especially important when k is equal to 3 because the denominator of skewness (a parameter to describe non-centrality of a distribution) is σ3.
- Keywords : Empirical influence function, influence function, outlier, sample influence function, skewness, statistics
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