Automatic Detection of Significant Areas for Functional Data with
  Directional Error Control

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Abstract

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 large-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.

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A comparison of the two one-sided tests procedure and the power approach for assessing the equivalence of average bioavailability.

Donald Schuirmann (1987)

The statistical test of hypothesis of no difference between the average bioavailabilities of two drug formulations, usually supplemented by an assessment of what the power of the statistical test would have been if the true averages had been inequivalent, continues to be used in the statistical analysis of bioavailability/bioequivalence studies. In the present article, this Power Approach (which in practice usually consists of testing the hypothesis of no difference at level 0.05 and requiring an estimated power of 0.80) is compared to another statistical approach, the Two One-Sided Tests Procedure, which leads to the same conclusion as the approach proposed by Westlake based on the usual (shortest) 1-2 alpha confidence interval for the true average difference. It is found that for the specific choice of alpha = 0.05 as the nominal level of the one-sided tests, the two one-sided tests procedure has uniformly superior properties to the power approach in most cases. The only cases where the power approach has superior properties when the true averages are equivalent correspond to cases where the chance of concluding equivalence with the power approach when the true averages are not equivalent exceeds 0.05. With appropriate choice of the nominal level of significance of the one-sided tests, the two one-sided tests procedure always has uniformly superior properties to the power approach. The two one-sided tests procedure is compared to the procedure proposed by Hauck and Anderson.