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http://dx.doi.org/10.5351/KJAS.2020.33.5.527

A study on the difference and calibration of empirical influence function and sample influence function  

Kang, Hyunseok (Daejeon High School)
Kim, Honggie (Department of Information and Statistics, Chungnam National University)
Publication Information
The Korean Journal of Applied Statistics / v.33, no.5, 2020 , pp. 527-540 More about this Journal
Abstract
While analyzing data, researching outliers, which are out of the main tendency, is as important as researching data that follow the general tendency. In this study we discuss the influence function for outlier discrimination. We derive sample influence functions of sample mean, sample variance, and sample standard deviation, which were not directly derived in previous research. The results enable us to mathematically examine the relationship between the empirical influence function and sample influence function. We can also consider a method to approximate the sample influence function by the empirical influence function. Also, the validity of the relationship between the approximated sample influence function and the empirical influence function is also verified by the simulation of random sampled data in normal distribution. As the result of a simulation, both the relationship between the two influence functions, sample and empirical, and the method of approximating the sample influence function through the emperical influence function were verified. This research has significance in proposing a method that reduces errors in the approximation of the empirical influence function and in proposing an effective and practical method that proceeds from previous research that approximates the sample influence function directly through empirical influence function by constant revision.
Keywords
influence function; outlier; empirical influence function; sample influence function;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Lee, H. and Kim, H. (2008). Influence function on the coefficient of variation, Communications for Statistical Applications and Methods, 15, 509-516.   DOI
2 Park, S. and Kim, H. (2019). A study on the location of the observation which has the least effect on the t-statistic, Journal of the Korean Data & Information Science Society, 30, 1221-1232.   DOI
3 Campbell, N. A. (1978). The influence function as an aid outlier detection in discrimination analysis, Applied Statistics, 27, 251-258.   DOI
4 Cook, R. D. (1977). Detection of influential observation in linear regression, Technometrics, 19, 15-18.   DOI
5 Cook, R. D. and Weisberg, S. (1980). Characterization of and empirical influence function for detection influential cases in regression, Technometrics, 22, 495-508.   DOI
6 Cook, R. D. and Weisberg, S. (1982). Residual and Influence in Regression, Chapman ad Hall, New York.
7 Critchley, F. (1985). Influence in principal components analysis, Biometika, 72, 627-636.   DOI
8 Hampel, F. R. (1974). The influence curve and its role in robust estimation, Journal of the American Statistical Association, 69, 383-393.   DOI
9 Kim, H. (1998). A study on cell influence to chi-square statistic in contingency tables, The Korean Communications in Statistics, 5, 35-42.
10 Radhakrishnan, R. and Kshirsagar, A. M. (1981). Influence functions for certain parameters in multi-variate analysis, Communications in Statistics, 10, 515-529.   DOI
11 Kim, H. and Lee, H. (1996). Influence Functions on ${\chi}^2$ statistic in contingency tables, The Korean Communications in Statistics, 3, 69-76.
12 Kim, H. and Kim, K. (2005). Influence of an observation on the t-statistic, The Korean Communications in Statistics, 12, 453-462.
13 Kim, S. and Kim, H. (2019). A study on the performance of the influence function on the t-statistic depending on population distributions, Journal of the Korean Data & Information Science Society, 30, 573-585.   DOI
14 Lee, H. and Kim, H. (2003). The changes in statistic when a row is deleted from a contingency table, The Korean Communications in Statistics, 10, 305-317.