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경험적 영향함수와 표본영향함수의 차이 및 보정에 관한 연구

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

  • 투고 : 2020.05.20
  • 심사 : 2020.07.03
  • 발행 : 2020.10.31

초록

이상치에 대한 적절한 선별과 배제없이 모든 데이터를 종합적으로 분석하게 되는 경우 데이터 분석을 통해 얻은 결과의 신뢰성과 해석의 일반성에 치명적인 위협을 받을 수 있다. 따라서 데이터의 분석 과정에서 이러한 이상치를 판별하고, 이상치가 통계량, 통계적 모형에 어떠한 영향을 주는 지에 대한 분석은 매우 중요한 일이라 할 수 있다. Hampel이 영향함수를 활용하여 이상치를 판별할 수 있는 방법을 소개한 이후, 이상치를 판별하기 위한 방법론으로 영향함수가 폭넓게 활용되어 왔다. 영향함수에는 경험적 영향함수와 표본영향함수가 있으며, 경험적 영향함수를 활용해 표본영향함수를 근사 추론하여 하나의 관측값이 제거되었을 때 통계량에 미치는 영향을 예측하는 방법론이 주로 활용되었다. 본 연구에서는 표본평균, 표본분산, 표본표준편차의 표본영향함수 유도를 통해 경험적 영향함수와 표본영향함수의 차이를 살펴 본다. 또한 경험적 영향함수로 표본영향함수를 근사하는 과정에서 발생하는 오차를 줄이기 위해 경험적 영향함수의 보정으로 표본영향함수를 근사 추론하는 방법을 제안하고, 모의실험을 통해 제안한 추론 방법의 타당성을 확인한다.

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.

키워드

참고문헌

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