응용통계연구 (The Korean Journal of Applied Statistics)

  • 제26권5호
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  • Pages.747-758
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  • 2013
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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고차원 데이터에서 공분산행렬의 추정에 대한 비교연구

A Comparative Study of Covariance Matrix Estimators in High-Dimensional Data

  • 투고 : 2013.07.29
  • 심사 : 2013.09.30
  • 발행 : 2013.10.31
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⟨ 이전 논문 다음 논문 ⟩

초록

공분산 행렬은 다변량 통계분석에서 중요한 역할을 하고 있으며 전통적인 다변량 분석의 경우 표본 공분산 행렬이 참공분산 행렬의 추정량으로 주로 사용되었다. 하지만 변수의 수가 표본의 크기보다 훨씬 큰 고차원 데이터와 같은 경우에는 표본 공분산 행렬은 비정칙행렬이 되어 기존의 다변량 기법을 사용하는 데 적절하지 않을 수가 있다. 최근 이러한 문제점을 해결하기 위해 축소추정, 경계추정, 수정 콜레스키 분해 추정 등의 새로운 공분산 행렬의 추정량들이 제안되었다. 본 논문에서는 추정량들의 성능에 영향을 미칠 수 있는 여러 현실적인 상황들을 가정하여 모의실험을 통해 참공분산 행렬의 추정량들의 성능을 비교하였다.

The covariance matrix is important in multivariate statistical analysis and a sample covariance matrix is used as an estimator of the covariance matrix. High dimensional data has a larger dimension than the sample size; therefore, the sample covariance matrix may not be suitable since it is known to perform poorly and event not invertible. A number of covariance matrix estimators have been recently proposed with three different approaches of shrinkage, thresholding, and modified Cholesky decomposition. We compare the performance of these newly proposed estimators in various situations.

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