Improved Stepdown Methods for Asymptotic Control of Generalized Error Rates

• Activity Number: 129
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Grayson Calhoun*+
• Companies: Iowa State University
• Keywords: Multiple testing ; bootstrap ; familywise error rate ; false discovery proportion ; partial identification ; moment inequalities

Abstract

This paper proposes new stepdown methods for testing multiple hypotheses and constructing confidence intervals while controlling the familywise error rate and other generalized error rates. One method is a refinement of Romano and Wolf's StepM (2005, Econometrica) that also removes inequalities that fall outside any n^{-1/2}-neighborhood of binding; it has the advantage that the threshold construction is incorporated into the stepdown procedure so it accounts for the number of total hypotheses (leading to better size control than some alternative methods) and excludes more nonbinding inequalities (leading to higher power). This method can also be used to test multiple inequality hypotheses simultaneously and construct confidence intervals for partially identified parameters. The paper presents methods for controlling the k-familywise error rate and the False Discovery Proportion for families of one and two-sided hypotheses as well. The paper also provides Monte Carlo evidence that the methods perform well in finite samples.