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Adaptive combination of dependent tests

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  • Sexton, Joseph
  • Blomhoff, Rune
  • Karlsen, Anette
  • Laake, Petter

Abstract

The construction of a multivariate two sample test is considered. An attractive approach to this problem, for instance when the data contain missing values or the number of variables is large, is to form an overall test by combining the componentwise test statistics. This can be done via their p-values or some other transformation. An important problem is how to perform the combination, as the relative power of a given combination will depend on the unknown true alternative. Recently, an approach has been proposed that makes use of the data to identify an appropriate combination. The method forms a pool of potential combinations of the componentwise p-values, setting the overall test statistic to the minimum p-value across the pool. One drawback of the approach, however, is that it does not utilize dependence between the componentwise tests, and thus potentially ignores valuable information. This issue is addressed, and two approaches are described that make use of the data to (1) determine which tests to combine; and (2) how best to utilize the between test statistic dependence. Simulations show that the proposed methods can lead to a substantial increase in power. An application to a dietary intervention study is given.

Suggested Citation

  • Sexton, Joseph & Blomhoff, Rune & Karlsen, Anette & Laake, Petter, 2012. "Adaptive combination of dependent tests," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1935-1943.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:6:p:1935-1943
    DOI: 10.1016/j.csda.2011.11.018
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    References listed on IDEAS

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    1. Yujun Wu & Marc G. Genton & Leonard A. Stefanski, 2006. "A Multivariate Two-Sample Mean Test for Small Sample Size and Missing Data," Biometrics, The International Biometric Society, vol. 62(3), pages 877-885, September.
    2. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the two-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 639-648, January.
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    4. Baringhaus, L. & Franz, C., 2004. "On a new multivariate two-sample test," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 190-206, January.
    5. Loughin, Thomas M., 2004. "A systematic comparison of methods for combining p-values from independent tests," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 467-485, October.
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