Abstract
In this paper we describe a coherent multiple testing procedure for correlated test statistics such as are encountered in functional linear models. The procedure makes use of two different p value combination methods: the Fisher combination method and the Šidák correction-based method. p values for Fisher’s and Šidák’s test statistics are estimated through resampling to cope with the correlated tests. Building upon these two existing combination methods, we propose the smallest p value as a new test statistic for each hypothesis. The closure principle is incorporated along with the new test statistic to obtain the overall p value and appropriately adjust the individual p values. Furthermore, a shortcut version for the proposed procedure is detailed, so that individual adjustments can be obtained even for a large number of tests. The motivation for developing the procedure comes from a problem of point-wise inference with smooth functional data where tests at neighboring points are related. A simulation study verifies that the methodology performs well in this setting. We illustrate the proposed method with data from a study on the aerial detection of the spectral effect of below ground carbon dioxide leakage on vegetation stress via spectral responses.
Original language | English |
---|---|
Pages (from-to) | 45-59 |
Number of pages | 15 |
Journal | Environmental and Ecological Statistics |
Volume | 22 |
Issue number | 1 |
DOIs | |
State | Published - Mar 2015 |
Bibliographical note
Publisher Copyright:© 2014, Springer Science+Business Media New York.
Keywords
- Combining correlated p values
- Functional data analysis
- Multiple testing
- Permutation procedure
ASJC Scopus subject areas
- Statistics and Probability
- General Environmental Science
- Statistics, Probability and Uncertainty