Two samples tests for functional data

Chongqi Zhang*, Heng PENG, Jin Ting Zhang

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

37 Citations (Scopus)


Data in many experiments arises as curves and therefore it is natural to use a curve as a basic unit in the analysis, which is in terms of functional data analysis (FDA). Functional curves are encountered when units are observed over time. Although the whole function curve itself is not observed, a sufficiently large number of evaluations, as is common with modern recording equipment, is assumed to be available. In this article, we consider the statistical inference for the mean functions in the two samples problem drawn from functional data sets, in which we assume that functional curves are observed, that is, we consider the test if these two groups of curves have the same mean functional curve when the two groups of curves without noise are observed. The L2-norm based and bootstrap-based test statistics are proposed. It is shown that the proposed methodology is flexible. Simulation study and real-data examples are used to illustrate our techniques.

Original languageEnglish
Pages (from-to)559-578
Number of pages20
JournalCommunications in Statistics - Theory and Methods
Issue number4
Publication statusPublished - Jan 2010

Scopus Subject Areas

  • Statistics and Probability

User-Defined Keywords

  • Bootstrap-based test statistic
  • Functional data
  • Hypothesis test
  • L2-norm-based test statistic


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