In this paper, we present inferential procedures to compare the means of two samples of functional data. The proposed tests are based on a suitable generalization of Mahalanobis distance to the Hilbert space of square integrable functions defined on a compact interval. The only conditions required concern the moments and the independence of the functional data, while the distribution of the processes generating the data is not needed to be specified. Test procedures are proposed for both the cases of known and unknown variance–covariance structures, and asymptotic properties of test statistics are deeply studied. A simulation study and a real case data analysis are also presented.

Statistical inference for stochastic processes: two-sample hypothesis tests / A. Ghiglietti, F. Ieva, A.M. Paganoni. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - 180(2017), pp. 49-68. [10.1016/j.jspi.2016.08.004]

Statistical inference for stochastic processes: two-sample hypothesis tests

A. Ghiglietti
;
F. Ieva
Secondo
;
2017

Abstract

In this paper, we present inferential procedures to compare the means of two samples of functional data. The proposed tests are based on a suitable generalization of Mahalanobis distance to the Hilbert space of square integrable functions defined on a compact interval. The only conditions required concern the moments and the independence of the functional data, while the distribution of the processes generating the data is not needed to be specified. Test procedures are proposed for both the cases of known and unknown variance–covariance structures, and asymptotic properties of test statistics are deeply studied. A simulation study and a real case data analysis are also presented.
Functional data; Distances in L-2; Hypothesis tests; Two-sample problems
Settore MAT/06 - Probabilita' e Statistica Matematica
Settore SECS-S/01 - Statistica
24-ago-2016
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/463997
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