TY - JOUR
T1 - Interval-wise testing for functional data
AU - Pini, A.
AU - Pini, Alessia
AU - Vantini, S.
PY - 2017
Y1 - 2017
N2 - 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.
AB - 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.
KW - Inference
KW - Statistics and Probability
KW - Statistics, Probability and Uncertainty
KW - canadian temperatures
KW - domain selection
KW - functional data
KW - Inference
KW - Statistics and Probability
KW - Statistics, Probability and Uncertainty
KW - canadian temperatures
KW - domain selection
KW - functional data
UR - http://hdl.handle.net/10807/119602
UR - http://www.tandf.co.uk/journals/titles/10485252.html
U2 - 10.1080/10485252.2017.1306627
DO - 10.1080/10485252.2017.1306627
M3 - Article
SN - 1048-5252
VL - 29
SP - 407
EP - 424
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
ER -