“Whoa! It's like Spotify but for academic articles.”

Instant Access to Thousands of Journals for just $40/month

Get 2 Weeks Free

Family-wise error rate of a step-down procedure

Multidimensional statistics, especially in the case where the sample size and the number of estimated parameters (or hypotheses tested) are comparable, is a natural area of application of the theory of random matrices (see V. L. Girko, Statistical Analysis of Observations of Increasing Dimension (Theory and Decision Library B). Springer, New York, 1995.). In this paper we consider procedures for multiple hypothesis testing that may be used in the case, which is even further from the classical statistics: the number of hypotheses may be much larger than the sample size. We consider general step-down multiple testing procedures – stopping-time-like decision rules that reject hypotheses sequentially, starting from those with the smallest (most significant) p -values. The most frequently used subclass of step-down procedures is that of threshold step-down (TSD) procedures exemplified by the classical Holm procedure. We obtain a formula that, for any step-down procedure satisfying a natural condition of monotonicity , provides the exact level at which the procedure controls the family-wise error rate – the probability of one or more false rejections. No assumptions are made about the joint distribution of p -values. The quantity is given by an easily computable expression. The result may be useful in all applications, where no parametric or other assumptions about the joint distribution of p -values can be legitimately made. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Random Operators and Stochastic Equations de Gruyter

Loading next page...

You're reading a free preview. Subscribe to read the entire article.

And millions more from thousands of peer-reviewed journals, for just $40/month

Get 2 Weeks Free

To be the best researcher, you need access to the best research

  • With DeepDyve, you can stop worrying about how much articles cost, or if it's too much hassle to order — it's all at your fingertips. Your research is important and deserves the top content.
  • Read from thousands of the leading scholarly journals from Springer, Elsevier, Nature, IEEE, Wiley-Blackwell and more.
  • All the latest content is available, no embargo periods.

Stop missing out on the latest updates in your field

  • We’ll send you automatic email updates on the keywords and journals you tell us are most important to you.
  • There is a lot of content out there, so we help you sift through it and stay organized.