The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Comparison of the covariance matrix for general linear model

일반 선형 모형에 대한 공분산 행렬의 비교

  • Nam, Sang Ah (Department of Statistics, Sungkyunkwan University) ;
  • Lee, Keunbaik (Department of Statistics, Sungkyunkwan University)
  • Received : 2016.10.18
  • Accepted : 2016.12.29
  • Published : 2017.02.28
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Abstract

In longitudinal data analysis, the serial correlation of repeated outcomes must be taken into account using covariance matrix. Modeling of the covariance matrix is important to estimate the effect of covariates properly. However, It is challenging because there are many parameters in the matrix and the estimated covariance matrix should be positive definite. To overcome the restrictions, several Cholesky decomposition approaches for the covariance matrix were proposed: modified autoregressive (AR), moving average (MA), ARMA Cholesky decompositions. In this paper we review them and compare the performance of the approaches using simulation studies.

경시적 자료분석에서 공변량 효과를 추정할 때 반복 측정된 결과들의 상관성은 고려되어야 한다. 따라서 공분산 행렬을 모형화하는 것은 매우 중요하다. 그러나 공분산 행렬의 추정은 모수들의 수가 많고 추정된 공분산행렬이 양정치성을 만족해야 하므로 쉽지 않은 문제이다. 이러한 제한을 극복하기 위해, 공분산행렬의 모형화를 위한 여러가지 방법을 제안하였다: 자기회귀/이동평균/자기회귀-이동평균 구조를 각각 적용한 수정 콜레스키분해 (Pourahmadi, 1999), 이동평균 콜레스키분해 (Zhang과 Leng, 2012)와 자기회귀-이동평균 콜레스키 분해 (Lee 등, 2017) 이들 구조를 가지는 공분산 행렬의 특징을 비교연구하고자 한다. 이 세 가지 모형의 성능을 비교하기 위한 모의실험을 실시한다.

Keywords

References

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