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Distribution-free tests for no effect of treatment in heteroscedastic functional data under both weak and long range dependence

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  • Wang, Haiyan
  • Higgins, James
  • Blasi, Dale

Abstract

In this paper, we present distribution-free tests to evaluate the effect of multiple treatments when there are a large number of repeated measurements from each subject nested in a treatment. We formulate new test statistics to account for heteroscedasticity and unbalanced designs. The asymptotic distributions for the test statistics are obtained when the repeated measurements from the same subject have long range dependence and weak dependence, respectively. The asymptotic results hold under the nonclassical setting in which the number of repeated measurements is large while the number of subjects per treatment may be small. A real application to compare cattle ear temperature profiles under different antibiotic treatments is given for illustration. Simulation studies are undertaken to compare the empirical performance of the proposed tests to commonly used methods.

Suggested Citation

  • Wang, Haiyan & Higgins, James & Blasi, Dale, 2010. "Distribution-free tests for no effect of treatment in heteroscedastic functional data under both weak and long range dependence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 390-402, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:390-402
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    References listed on IDEAS

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    1. Haiyan Wang & Michael Akritas, 2010. "Inference from heteroscedastic functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 149-168.
    2. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
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    4. X. Lin & D. Zhang, 1999. "Inference in generalized additive mixed modelsby using smoothing splines," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 381-400, April.
    5. Simon N. Wood, 2008. "Fast stable direct fitting and smoothness selection for generalized additive models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(3), pages 495-518, July.
    6. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
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    Cited by:

    1. Wang, Haiyan & Akritas, Michael G., 2010. "Rank test for heteroscedastic functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1791-1805, September.
    2. Harrar, Solomon W. & Kong, Xiaoli, 2016. "High-dimensional multivariate repeated measures analysis with unequal covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 1-21.

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