Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis |
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| Authors: | Ana‐Maria Staicu Yingxing Li Ciprian M Crainiceanu David Ruppert |
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| Institution: | 1. Department of Statistics, North Carolina State University;2. The Wang Yanan Institute for Studies in Economics, Xiamen University;3. Department of Biostatistics, Johns Hopkins University;4. Department of Statistical Science and School of Operations Research and Information Engineering, Cornell University |
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| Abstract: | 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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| Keywords: | functional data longitudinal data pseudo‐likelihood sleep health heart study two‐sample problem |
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