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October 20 Math Colloquium

Bo Li, The Citadel

Robust Step-down Method for Multiple Hypothesis Testing in Linear Models

In this talk we propose a rank statistic step-down method strongly controls family wise error rate in general linear models. Westfall and Young’s stepdown method relies on the assumption of subset piv- otality. Subset pivotality may not hold true in some cases. Since a key component of step-down method is monotonicity of critical values. We use percentiles of maximum modulus statistics as critical values at each step of the step-down method. The probability distribution generating data is often unknown in practice. Bootstrap method is used to estimate the successive critical values. The asymptotic results of proposed method are derived. Least square method is known to be sensitive to violation of normality assumption and outlier influence. Rank based method is a robust alternative. The stability of the fi- nite sample properties of bootstrap step-down method based on rank statistics is studied by comparing the empirical error rates with those of the method based on least square statistics. Simulation study shows rank statistic based bootstrap stepdown method controls family wise error rate in strong sense under a variety of distributions. Simulation also shows Westfall and Young’s bootstrap stepdown method controls family wise error rate in weak sense.

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