The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Nonparametric test on dimensionality of explantory variables

설명변수 차원 축소에 관한 비모수적 검정

  • 서한손 ((133-701) 서울시 광진구 모진동 93-1, 건국대학교 상경대학 응용통계학과)
  • Published : 1995.09.01
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Abstract

For the determination of dimension of e.d.r. space, both of Sliced Inverse Regression (SIR) and Principal Hessian Directions (PHD) proposed asymptotic test. But the asymptotic test requires the normality and large samples of explanatory variables. Cook and Weisberg(1991) suggested permutation tests instead. In this study permutation tests are actually made, and the power of them is compared with asymptotic test in the case of SIR and PHD.

설명변수 축소방법들인 Sliced Inverse Regression과 Principal Hessian Directions에서는 효과적 차원축소공간의 차원을 결정하기 위하여 설명변수의 정규성과 충분한 수의 자료가 요구되는 점근적검정(asymptotic test)을 제시하고 있다. 본 연구에서는 Cook과 Weisberg(1991)가 제안하였던 순열검정통계량(permutation test statistic)을 개발하여 SIR과 PHD에서 제시된 점근적 검정 통계량과 검정력을 비교하기로 한다.

Keywords

References

  1. Journal of the American Statistical Association v.86 Discussion of "Sliced inverse regression" by K.C.Li. Cook,R.D.;Weisberg,S.
  2. Introduction to Regression Graphics Cook,R.D.;Weisberg,S.
  3. Multivariate Statistical Simulation Johnson,M.
  4. Journal of the American Statistical Association v.86 Sliced inverse regression for dimension reduction(with discussion) Li,K.C.
  5. Journal of the American Statistical Association v.87 On principal Hessian directions for data visualization and dimension reduction: another application of Stein's lemma, Li,K.C.
  6. The Annals of Statistics v.9 Estimation of the Mean of a Multivariate Normal Distribution Stein,C.