Two sample inference for the second-order property of temporally dependent functional data

Xianyang Zhang, Xiaofeng Shao

Research output: Contribution to journalArticlepeer-review


Motivated by the need to statistically quantify the difference between two spatio-temporal datasets that arise in climate downscaling studies, we propose new tests to detect the differences of the covariance operators and their associated characteristics of two functional time series. Our two sample tests are constructed on the basis of functional principal component analysis and self-normalization, the latter of which is a new studentization technique recently developed for the inference of a univariate time series. Compared to the existing tests, our SN-based tests allow for weak dependence within each sample and it is robust to the dependence between the two samples in the case of equal sample sizes. Asymptotic properties of the SNbased test statistics are derived under both the null and local alternatives. Through extensive simulations, our SN-based tests are shown to outperform existing alternatives in size and their powers are found to be respectable. The tests are then applied to the gridded climate model outputs and interpolated observations to detect the difference in their spatial dynamics.

Original languageEnglish (US)
Pages (from-to)909-929
Number of pages21
Issue number2
StatePublished - May 1 2015


  • Climate downscaling
  • Functional data analysis
  • Long run variance matrix
  • Self-normalization
  • Time series
  • Two sample problem

ASJC Scopus subject areas

  • Statistics and Probability


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