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.
Original language | English (US) |
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Pages (from-to) | 932-949 |
Number of pages | 18 |
Journal | Scandinavian Journal of Statistics |
Volume | 41 |
Issue number | 4 |
DOIs | |
State | Published - Dec 1 2014 |
Keywords
- Functional data
- Longitudinal data
- Pseudo-likelihood
- Sleep health heart study
- Two-sample problem
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty