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\centerline{\bf STANFORD UNIVERSITY}
\centerline{\bf DEPARTMENT OF STATISTICS}
\centerline{\big DEPARTMENTAL SEMINAR}
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\centerline{4:15 p.m., Tuesday, September 28, 2004}
\centerline{Sequoia Hall Room 200}
\centerline{(Cookies at 3:45 in 1st Floor Lounge)}

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\centerline{\sl Joe Romano}
\centerline{\sl Stanford University}
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\centerline{\bf Error Control in Multiple Testing}
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Abstract:

(This talk is  based  on  collaborations  with Erich   Lehmann, Juliet
Shaffer, and Michael Wolf.)

Consider the multiple testing problem of testing $s$ null
hypotheses. In this talk, various stepwise methods are constructed
under constraints of various notions of error control.

In the first part of the talk, we assume a parametric family of
distributions which satisfies a certain monotonicity
assumption.Attention is restricted to procedures that control the
familywise error rate (FWE) in the strong sense and which satisfy a
monotonicity condition. Under these assumptions, we prove certain
maximin optimality results for the well-known stepdown and stepup
procedures.

In the second part, we consider the general problem of contructing
methods that control the FWE in a general (nonparametric) setting.In
order to improve upon the Bonferroni method or Holm's (1979) stepdown
method, Westfall and Young (1993) make effective 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. We will show how to construct
methods that control the FWE, both in finite and large samples. A key
ingredient is monotonicity of critical values which allows one to
effectively reduce the multiple testing problem of controlling the FWE
to the single testing problem of controlling the probability of a Type
1 error. Resampling methods are then incorporated into the stepwise
schemes.

In the final part of the talk, alternative measures of error control
will be discussed. Explicit construction of stepwise procedures for
these alternative methods will be presented as well.

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