Paper #727

Título:

Exact and approximate stepdown methods for multiple hypothesis testing

Autores:

Joseph Romano y Michael Wolf

Fecha:

Diciembre 2003

Resumen:

Consider 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 eective 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.

Palabras clave:

Bootstrap, familywise error rate, multiple testing, permutation test, randomization test, stepdown procedure, subsampling

Códigos JEL:

C12, C14

Área de investigación:

Estadística, Econometría y Métodos Cuantitativos

Publicado en:

Journal of the American Statistical Association 100, 94-108, 2005

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