To detect differences between the mean curves of two samples in longitudinal study or functional data analysis, we usually need to partition the temporal or spatial domain into several pre-determined sub-areas. In this paper we apply the idea of larg
e-scale multiple testing to find the significant sub-areas automatically in a general functional data analysis framework. A nonparametric Gaussian process regression model is introduced for two-sided multiple tests. We derive an optimal test which controls directional false discovery rates and propose a procedure by approximating it on a continuum. The proposed procedure controls directional false discovery rates at any specified level asymptotically. In addition, it is computationally inexpensive and able to accommodate different time points for observations across the samples. Simulation studies are presented to demonstrate its finite sample performance. We also apply it to an executive function research in children with Hemiplegic Cerebral Palsy and extend it to the equivalence tests.
Rejoinder to Likelihood Inference for Models with Unobservables: Another View by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
There have been controversies among statisticians on (i) what to model and (ii) how to make inferences from models with unobservables. One such controversy concerns the difference between estimation methods for the marginal means not necessarily havi
ng a probabilistic basis and statistical models having unobservables with a probabilistic basis. Another concerns likelihood-based inference for statistical models with unobservables. This needs an extended-likelihood framework, and we show how one such extension, hierarchical likelihood, allows this to be done. Modeling of unobservables leads to rich classes of new probabilistic models from which likelihood-type inferences can be made naturally with hierarchical likelihood.
