Interval-wise testing for functional data

A. Pini and S. Vantini

Journal of Nonparametric Statistics, 2017, vol. 29, issue 2, 407-424

Abstract: In the framework of null hypothesis significance testing for functional data, we propose a procedure able to select intervals of the domain imputable for the rejection of a null hypothesis. An unadjusted p-value function and an adjusted one are the output of the procedure, namely interval-wise testing. Depending on the sort and level α of type-I error control, significant intervals can be selected by thresholding the two p-value functions at level α. We prove that the unadjusted (adjusted) p-value function point-wise (interval-wise) controls the probability of type-I error and it is point-wise (interval-wise) consistent. To enlighten the gain in terms of interpretation of the phenomenon under study, we applied the interval-wise testing to the analysis of a benchmark functional data set, i.e. Canadian daily temperatures. The new procedure provides insights that current state-of-the-art procedures do not, supporting similar advantages in the analysis of functional data with less prior knowledge.

Date: 2017
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Citations: View citations in EconPapers (15)

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DOI: 10.1080/10485252.2017.1306627

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