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Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis

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  • Ana-Maria Staicu
  • Yingxing Li
  • Ciprian M. Crainiceanu
  • David Ruppert

Abstract

type="main" xml:id="sjos12075-abs-0001"> This paper introduces a general framework for testing hypotheses about the structure of the mean function of complex functional processes. Important particular cases of the proposed framework are as follows: (1) testing the null hypothesis that the mean of a functional process is parametric against a general alternative modelled by penalized splines; and (2) testing the null hypothesis that the means of two possibly correlated functional processes are equal or differ by only a simple parametric function. A global pseudo-likelihood ratio test is proposed, and its asymptotic distribution is derived. The size and power properties of the test are confirmed in realistic simulation scenarios. Finite-sample power results indicate that the proposed test is much more powerful than competing alternatives. Methods are applied to testing the equality between the means of normalized δ-power of sleep electroencephalograms of subjects with sleep-disordered breathing and matched controls.

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  • Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:4:p:932-949
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    File URL: http://hdl.handle.net/10.1111/sjos.12075
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    References listed on IDEAS

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    3. Ming Xiong & Ao Yuan & Hong-Bin Fang & Colin O. Wu & Ming T. Tan, 2022. "Estimation and Hypothesis Test for Mean Curve with Functional Data by Reproducing Kernel Hilbert Space Methods, with Applications in Biostatistics," Mathematics, MDPI, vol. 10(23), pages 1-17, December.
    4. 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.
    5. Pini, Alessia & Sørensen, Helle & Tolver, Anders & Vantini, Simone, 2023. "Local inference for functional linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    6. Lee, Jihui & Li, Gen & Wilson, James D., 2020. "Varying-coefficient models for dynamic networks," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    7. Guochang Wang & Xiang-Nan Feng & Min Chen, 2016. "Functional Partial Linear Single-index Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 261-274, March.
    8. Pini, Alessia & Spreafico, Lorenzo & Vantini, Simone & Vietti, Alessandro, 2019. "Multi-aspect local inference for functional data: Analysis of ultrasound tongue profiles," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 162-185.
    9. Pini, Alessia & Stamm, Aymeric & Vantini, Simone, 2018. "Hotelling’s T2 in separable Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 284-305.
    10. Li, Yingxing & Huang, Chen & Härdle, Wolfgang K., 2019. "Spatial functional principal component analysis with applications to brain image data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 263-274.
    11. Konrad Abramowicz & Alessia Pini & Lina Schelin & Sara Sjöstedt de Luna & Aymeric Stamm & Simone Vantini, 2023. "Domain selection and familywise error rate for functional data: A unified framework," Biometrics, The International Biometric Society, vol. 79(2), pages 1119-1132, June.
    12. Yingxing Li & Chen Huang & Wolfgang Karl Härdle, 2017. "Spatial Functional Principal Component Analysis with Applications to Brain Image Data," SFB 649 Discussion Papers SFB649DP2017-024, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Rafael Meléndez & Ramón Giraldo & Víctor Leiva, 2020. "Sign, Wilcoxon and Mann-Whitney Tests for Functional Data: An Approach Based on Random Projections," Mathematics, MDPI, vol. 9(1), pages 1-11, December.
    14. Gao, Yuhe & Shi, Chengchun & Song, Rui, 2023. "Deep spectral Q-learning with application to mobile health," LSE Research Online Documents on Economics 119445, London School of Economics and Political Science, LSE Library.
    15. Gina-Maria Pomann & Ana-Maria Staicu & Sujit Ghosh, 2016. "A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 395-414, April.
    16. Alexander S. Long & Brian J. Reich & Ana‐Maria Staicu & John Meitzen, 2023. "A nonparametric test of group distributional differences for hierarchically clustered functional data," Biometrics, The International Biometric Society, vol. 79(4), pages 3778-3791, December.

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