응용통계연구 (The Korean Journal of Applied Statistics)

  • 제18권2호
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  • Pages.381-393
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  • 2005
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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분할 역회귀모형에서 차원결정을 위한 점근검정법

Asymptotic Test for Dimensionality in Sliced Inverse Regression

  • 박종선 (성균관대학교 경제학부 통계학전공) ;
  • 곽재근 (성균관대학교 경제학부 통계학전공)
  • 발행 : 2005.07.01
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초록

회귀모형에서 필요한 설명변수들의 선형결합들을 탐색하기 위한 방법 중의 하나로 분할역회귀모형을 들 수 있다. 이러한 분할역회귀모형에서 모형에 필요한 설명변수들의 선형결합의 수, 즉 차원을 결정하기 위한 여러 가지의 검정법들이 소개 되었으나 설명변수들의 정규성 가정을 필요로 하거나 다른 제약이 있다. 본 논문에서는 주성분분석에 대한 확률모형을 이 용하여 정규성가정을 필요로하지 않으며 분할의 수에 로버스트한 검정법을 소개하고 모의실험과 실제자료에 대한 적용결과를 통하여 기존의 검정법과 비교하였다.

As a promising technique for dimension reduction in regression analysis, Sliced Inverse Regression (SIR) and an associated chi-square test for dimensionality were introduced by Li (1991). However, Li's test needs assumption of Normality for predictors and found to be heavily dependent on the number of slices. We will provide a unified asymptotic test for determining the dimensionality of the SIR model which is based on the probabilistic principal component analysis and free of normality assumption on predictors. Illustrative results with simulated and real examples will also be provided.

키워드

참고문헌

  1. Anderson, T. W. (1963). Asymptotic theory for principal component analysis, Annals of Mathematical Statistics, 34, 122-148 https://doi.org/10.1214/aoms/1177704248
  2. Anderson, T. W., and Rubin, H. (1956). Statistical inference in factor analysis, In J. Newman (Ed.), Proceedings of the Third Berkeley Symposium on Mathematical Statistics and Probability, Volume V, U. Cal, Berkeley, 111-150
  3. Bura, E., and Cook, R. D. (2001). Extending SIR: The weighted chi-square test, Journal of the American Statistical Association, 96, 996-1003 https://doi.org/10.1198/016214501753208979
  4. Ferre, L. (1998). Determining the dimension in sliced inverse regression and related methods, Journal of the American Statistical Association, 93, 132-140 https://doi.org/10.2307/2669610
  5. Lawley, D. N. (1953). A modified method of estimation in factor analysis and some large sample results, In Uppsala Symposium on Psychological Factor Analysis, Number 3 in Nordisk Psykologi Monograph Series, 35-42. Uppsala: Almqvist and Wiksell
  6. Li, K. C. (1999). Sliced inverse regression for dimension reduction, Journal of the American Statistical Association, 86, 316-342 https://doi.org/10.2307/2290563
  7. Schott, J. R. (1994). Determining the dimensionality in sliced inverse regression, Journal of the American Statistical Association, 89, 141-148 https://doi.org/10.2307/2291210
  8. Tipping, M. E., and Bishop, C. M. (1999). Probabilisitic principal component analysis, Journal of the Royal Statistical Society, Series B, 61, 611-622 https://doi.org/10.1111/1467-9868.00196
  9. Vellilla, S. (1998). Assessing the number of linear components in a general regression problem, Journal of the American Statistical Association, 93, 1088-1098 https://doi.org/10.2307/2669852
  10. Whittle, P. (1952). On principal components and least square methods of factor analysis, Skamdinavisk Aktuarietidskrift, 36, 223-239
  11. Young, G. (1940). Maximum likelihood estimation and factor analysis, Psychometrika, 6, 49-53 https://doi.org/10.1007/BF02288574