Electronic Journal of Statistics

Admissible, consistent multiple testing with applications including variable selection

Chuanwen Chen, Arthur Cohen, and Harold B. Sackrowitz

Full-text: Open access

Abstract

For multivariate normal models and some exponential family models a multiple testing stepwise method is offered that is both admissible and consistent. The method is readily adaptable to selecting variables in linear regression models where it is akin to the forward selection method plus a screening stage plus a sign compatibility stage.

Article information

Source
Electron. J. Statist., Volume 3 (2009), 633-650.

Dates
First available in Project Euclid: 10 July 2009

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1247231686

Digital Object Identifier
doi:10.1214/09-EJS391

Mathematical Reviews number (MathSciNet)
MR2521214

Zentralblatt MATH identifier
1326.62041

Subjects
Primary: 62F03: Hypothesis testing
Secondary: 62C15: Admissibility 62J05: Linear regression

Keywords
backward method exponential family forward method linear regression step-down procedures step-up procedures variable selection

Citation

Chen, Chuanwen; Cohen, Arthur; Sackrowitz, Harold B. Admissible, consistent multiple testing with applications including variable selection. Electron. J. Statist. 3 (2009), 633--650. doi:10.1214/09-EJS391. https://projecteuclid.org/euclid.ejs/1247231686


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References

  • An, H. and Gu, L. (1985). On the selection of regression variables., Acta Mathematicae Applicatae Sinica 2, 27–36.
  • Benjamini, Y. and Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing., Journal of the Royal Statistical Society, Ser. B 57, 289–289.
  • Bunea, F., Wegkamp, M.H., and Auguste, A. (2006). Consistent variable selection in high dimensional regression via multiple testing., Journal of Statistical Planning and Inference 136, 12, 4349–4364.
  • Chen, C., Cohen, A., and Sackrowitz, H.B. (2009). Multiple testing in ordinal data models., Submitted.
  • Christensen, R. (1987)., Plane Answers to Complex Questions: The Theory of Linear Models. Springer.
  • Cohen, A. and Sackrowitz, H.B. (2005a). Decision theory results for one-sided multiple comparison procedures., The Annals of Statistics 33, 1, 126–144.
  • Cohen, A. and Sackrowitz, H.B. (2005b). Characterization of Bayes procedures for multiple endpoint problems and inadmissibility of the step-up procedure., The Annals of Statistics 33, 1, 145–158.
  • Cohen, A. and Sackrowitz, H.B. (2007). More on the inadmissibility of step-up., Journal of Multivariate Analysis 98, 3, 481–492.
  • Cohen, A. and Sackrowitz, H.B. (2008). Multiple testing to two-sided alternatives with dependent data., Statistica Sinica 18, 1593–1602.
  • Cohen, A., Kolassa, J., and Sackrowitz, H.B. (2007). A smooth version of the step-up procedure for multiple tests of hypotheses., Journal of Statistical Planning and Inference 137, 11, 3352–3360.
  • Cohen, A., Sackrowitz, H.B., and Xu, M. (2009). A new multiple testing method in the dependent case., The Annals of Statistics 37.
  • Dudoit, S. and Van Der Laan, M.J. (2008)., Multiple Testing Procedures with Applications to Genomics. Springer Verlag.
  • Johnson, N.L. and Kotz, S. (1970)., Continuous univariate distributions-2. Houghton Mifflin.
  • Lehmann, E.L. and Romano, J.P. (2005)., Testing Statistical Hypotheses, Third ed. Springer.
  • Matthes, T.K. and Truax, D.R. (1967). Tests of composite hypotheses for the multivariate exponential family., The Annals of Mathematical Statistics 38, 681–697.
  • Miller, A. (2002)., Subset Selection in Regression, Second ed. Chapman and Hall/CRC.