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2019 Vol.32, Issue 3 Preview Page
Comparison Study of Kernel Density Estimation according to Various Bandwidth Selectors

다양한 대역폭 선택법에 따른 커널밀도추정의 비교 연구

Young-Jin Kang1
,
Yoojeong Noh2†
강 영 진1
,
노 유 정2†
1Research Institute of Mechanical Technology, Pusan Nat’l Univ., Busan, 46241, Korea
2School of Mechanical Engineering, Pusan Nat’l Univ., Busan, 46241, Korea
1부산대학교 기계기술연구원
2부산대학교 기계공학부
†Corresponding author: Tel: +82-51-510-2308; E-mail: yoonoh@pusan.ac.kr
2019. pp. 173-181
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Abstract

To estimate probabilistic distribution function from experimental data, kernel density estimation(KDE) is mostly used in cases when data is insufficient. The estimated distribution using KDE depends on bandwidth selectors that smoothen or overfit a kernel estimator to experimental data. In this study, various bandwidth selectors such as the Silverman’s rule of thumb, rule using adaptive estimates, and oversmoothing rule, were compared for accuracy and conservativeness. For this, statistical simulations were carried out using assumed true models including unimodal and multimodal distributions, and, accuracies and conservativeness of estimating distribution functions were compared according to various data. In addition, it was verified how the estimated distributions using KDE with different bandwidth selectors affect reliability analysis results through simple reliability examples.

Keywords
bandwidth selector
kernel density estimation
multimodal distribution
reliability analysis
statistical modeling
unimodal distribution

제한된 실험 데이터로부터 확률분포함수를 추정하기 위해서 KDE가 많이 사용되고 있다. KDE에 의한 분포함수는 대역폭 선택법에 따라서 실험 데이터에 대해 평활하거나 과대적합된 커널 추정치를 생성한다. 본 연구에서는 Silverman’s rule of thumb, rule using adaptive estimate, oversmoothing rule을 사용해서 각 방법에 따른 정확성과 보수적인 성향을 비교하였 다. 비교를 위해서 단봉분포와 다봉분포를 가지는 실제 모델을 가정하고 통계적 시뮬레이션을 수행한 다음 다양한 데이터의 개수에 따른 추정된 분포함수의 정확도와 보수성을 비교하였다. 또한, 간단한 신뢰성 예제를 통해 대역폭 선택법에 따른 KDE의 추정된 분포가 신뢰성 해석 결과에 어떻게 영향을 미치는지 확인하였다.

키워드
다봉분포
단봉분포
대역폭 선택법
신뢰성 해석
커널밀도추정
통계 모델링
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Information
  • Publisher :Computational Structural Engineering Institute of Korea
  • Publisher(Ko) :한국전산구조공학회
  • Journal Title :Journal of the Computational Structural Engineering Institute of Korea
  • Journal Title(Ko) :한국전산구조공학회 논문집
  • Volume : 32
  • No :3
  • Pages :173-181
  • Received Date : 2019-03-11
  • Revised Date : 2019-04-03
  • Accepted Date : 2019-05-10
  • DOI :https://doi.org/10.7734/COSEIK.2019.32.3.173
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