Exact and approximate stepdown methods for multiple hypothesis testing
AbstractConsider the problem of testing k hypotheses simultaneously. In this paper, we discuss finite and large sample theory of stepdown methods that provide control of the familywise error rate (FWE). In order to improve upon the Bonferroni method or Holm's (1979) stepdown method, Westfall and Young (1993) make e ective use of resampling to construct stepdown methods that implicitly estimate the dependence structure of the test statistics. However, their methods depend on an assumption called subset pivotality. The goal of this paper is to construct general stepdown methods that do not require such an assumption. In order to accomplish this, we take a close look at what makes stepdown procedures work, and a key component is a monotonicity requirement of critical values. By imposing such monotonicity on estimated critical values (which is not an assumption on the model but an assumption on the method), it is demonstrated that the problem of constructing a valid multiple test procedure which controls the FWE can be reduced to the problem of contructing a single test which controls the usual probability of a Type 1 error. This reduction allows us to draw upon an enormous resampling literature as a general means of test contruction.
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Bibliographic InfoPaper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 727.
Date of creation: Dec 2003
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Web page: http://www.econ.upf.edu/
Bootstrap; familywise error rate; multiple testing; permutation test; randomization test; stepdown procedure; subsampling;
Other versions of this item:
- Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, Elsevier, vol. 73(2), pages 241-250, November.
- G. Hommel, 1986. "Multiple test procedures for arbitrary dependence structures," Metrika, Springer, Springer, vol. 33(1), pages 321-336, December.
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