Statistical inference for stochastic processes: Two-sample hypothesis tests

Andrea Ghiglietti, Francesca Ieva, Anna Maria Paganoni

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)49-68
Number of pages20
JournalJournal of Statistical Planning and Inference
Publication statusPublished - 2017
Externally publishedYes


  • Distances in L2
  • Functional data
  • Hypothesis tests
  • Two-sample problems


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