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Rank test for heteroscedastic functional data

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  • Wang, Haiyan
  • Akritas, Michael G.

Abstract

In this paper, we consider (mid-)rank based inferences for testing hypotheses in a fully nonparametric marginal model for heteroscedastic functional data that contain a large number of within subject measurements from possibly only a limited number of subjects. The effects of several crossed factors and their interactions with time are considered. The results are obtained by establishing asymptotic equivalence between the rank statistics and their asymptotic rank transforms. The inference holds under the assumption of[alpha]-mixing without moment assumptions. As a result, the proposed tests are applicable to data from heavy-tailed or skewed distributions, including both continuous and ordered categorical responses. Simulation results and a real application confirm that the (mid-)rank procedures provide both robustness and increased power over the methods based on original observations for non-normally distributed data.

Suggested Citation

  • Wang, Haiyan & Akritas, Michael G., 2010. "Rank test for heteroscedastic functional data," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1791-1805, September.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:8:p:1791-1805
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    References listed on IDEAS

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    1. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
    2. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    3. 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.
    4. Thompson, G. L., 1990. "Asymptotic distribution of rank statistics under dependencies with multivariate application," Journal of Multivariate Analysis, Elsevier, vol. 33(2), pages 183-211, May.
    5. Haiyan Wang & Michael Akritas, 2010. "Inference from heteroscedastic functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 149-168.
    6. Harrar, Solomon W. & Bathke, Arne C., 2008. "Nonparametric methods for unbalanced multivariate data and many factor levels," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1635-1664, September.
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    Cited by:

    1. 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.
    2. 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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