Communications for Statistical Applications and Methods

  • 제20권2호
  • /
  • Pages.147-155
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  • 2013
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  • 2287-7843(pISSN)
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  • 2383-4757(eISSN)
한국통계학회 (The Korean Statistical Society)
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Permutation Predictor Tests in Linear Regression

  • Ryu, Hye Min (Clinical Research Coordination Center, National Cancer Center) ;
  • Woo, Min Ah (Korea Information and Communication Industry Institute) ;
  • Lee, Kyungjin (Department of Statistics, Ewha Womans University) ;
  • Yoo, Jae Keun (Department of Statistics, Ewha Womans University)
  • 투고 : 2013.02.19
  • 심사 : 2013.03.25
  • 발행 : 2013.03.31
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초록

To determine whether each coefficient is equal to zero or not, usual $t$-tests are a popular choice (among others) in linear regression to practitioners because all statistical packages provide the statistics and their corresponding $p$-values. Under smaller samples (especially with non-normal errors) the tests often fail to correctly detect statistical significance. We propose a permutation approach by adopting a sufficient dimension reduction methodology to overcome this deficit. Numerical studies confirm that the proposed method has potential advantages over the t-tests. In addition, data analysis is also presented.

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참고문헌

  1. Cook, R. D. (1998) Regression Graphics, Wiley, New York.
  2. Cook, R. D. andWeisberg, S. (1991). Discussion of sliced inverse regression for dimension reduction by K.C. Li. Journal of the American Statistical Association, 86, 328-332.
  3. Cook, R. D. and Weisberg, S. (1999). Applied Regression Including Computing and Graphics, Wiley, New York.
  4. Kutner, M. H., Nachtsheim, C. J., Neter, J. and Li, W. (2005). Applied Linear Statistical Models, 5th edition, McGraw-Hill/Irwin, New York.
  5. Yin, X. and Cook, R. D. (2002). Dimension reduction for the conditional kth moment in regression. Journal of Royal Statistical Society, Series B, 64, 159-175. https://doi.org/10.1111/1467-9868.00330