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Inference from heteroscedastic functional data

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  • Haiyan Wang
  • Michael Akritas

Abstract

Technological advancements have produced an abundance of data sets in which a large number of repeated measurements are observed within a subject or stratum. Many of these data sets are based on a small number of subjects rendering most existing inferential methods unsuitable. This paper develops test procedures based on a novel model for nested heteroscedastic high-dimensional data which we propose. The novelty of the model rests on the fact that the random effects are assumed to be neither uncorrelated nor normal. The model is nonparametric in the sense that it leaves the covariance structure unspecified and applies to both discrete and continuous data. The test procedures developed are useful for evaluating the effects of time as well as their interactions with the crossed factors on the stratum. The asymptotic theory of the test statistics is driven by a large number of measurements per subject and the assumption of nonstationary α-mixing on the error term. Simulation studies and real applications show that the proposed tests are more powerful in detecting effects compared with benchmark methods in data with very limited number of replications.

Suggested Citation

  • Haiyan Wang & Michael Akritas, 2010. "Inference from heteroscedastic functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 149-168.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:149-168
    DOI: 10.1080/10485250903171621
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    3. 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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    5. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    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. A. Pini & S. Vantini, 2017. "Interval-wise testing for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 407-424, April.
    3. 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.
    4. 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.
    5. Harrar, Solomon W. & Kong, Xiaoli, 2022. "Recent developments in high-dimensional inference for multivariate data: Parametric, semiparametric and nonparametric approaches," Journal of Multivariate Analysis, Elsevier, vol. 188(C).

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