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논문 기본 정보
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- 학위논문
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- 2020
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In modern society, data are being stacked at a tremendous speed. While analyzing these data, researching the outliers which are out of main tendency is as important as researching data which follow the general tendency. In this study we discuss influence function for outlier discrimination. Especially, we derive sample influence functions of sample mean, sample variance, sample standard deviation, and t-statistic which were not directly derived in previous researches. Throughout these results, we mathematically examine the relationship between empirical influence function and sample influence function, and consider the method to approximate sample influence function by empirical influence function. Also, the validity of relationship between approximated sample influence function and empirical influence function is verified by simulation of 300 random sampled data in normal distribution.
As a result of the simulation, the relationship between sample influence function which is derived from sample mean, sample variance, sample standard deviation, and t-statistics, and empirical influence function, and the method of approximating sample influence function through empirical influence function were verified.
This research has significance in proposing a method which reduces errors in approximation of empirical influence function and in proposing an effective and practical method that proceeds from previous research which approximates sample influence function directly through empirical influence function by constant revision.
As a result of the simulation, the relationship between sample influence function which is derived from sample mean, sample variance, sample standard deviation, and t-statistics, and empirical influence function, and the method of approximating sample influence function through empirical influence function were verified.
This research has significance in proposing a method which reduces errors in approximation of empirical influence function and in proposing an effective and practical method that proceeds from previous research which approximates sample influence function directly through empirical influence function by constant revision.
목차
1. 서론 12. 영향함수와 t통계량 52.1 영향함수의 정의 및 평균, 분산, 표준편차의 영향함수 52.2 t통계량에 대한 영향함수 102.3 다양한 통계량에 대한 경험적 영향함수와 표본영향함수의 정의 143. 경험적 영향함수와 표본영향함수의 관계 163.1 표본평균, 표본분산, 표본표준편차에 대한 표본영향함수 163.2 t통계량에 대한 표본영향함수 254. 모의실험을 통한 경험적 영향함수와 표본영향함수의 관계 확인 384.1 xbar_(i)-xbar의 근사 414.2 s²_(i)-s²의 근사 464.3 s_(i)-s의 근사 544.4 t_(i)-t의 근사 605. 결론 685.1 결론 685.2 향후 연구방향 71참고문헌 72ABSTRACT 75부록: 정규분포에서 추출된 표본 데이터 77
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