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.

Pini, A., Vantini, S., Interval-wise testing for functional data, <<JOURNAL OF NONPARAMETRIC STATISTICS>>, 2017; 29 (2): 407-424. [doi:10.1080/10485252.2017.1306627] [http://hdl.handle.net/10807/119602]

Interval-wise testing for functional data

Pini, Alessia
;
2017

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.
2017
Inglese
Pini, A., Vantini, S., Interval-wise testing for functional data, <<JOURNAL OF NONPARAMETRIC STATISTICS>>, 2017; 29 (2): 407-424. [doi:10.1080/10485252.2017.1306627] [http://hdl.handle.net/10807/119602]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/119602
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