Testing separability of space-time functional processes

P. Constantinou, P. Kokoszka, M. Reimherr

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Separability is a common simplifying assumption on the covariance structure of spatiotemporal functional data. We present three tests of separability one a functional extension of the Monte Carlo likelihood method of Mitchell et al. (2006) and two based on quadratic forms. Our tests are based on asymptotic distributions of maximum likelihood estimators and do not require Monte Carlo simulation. The main theoretical contribution of this paper is the specification of the joint asymptotic distribution of these estimators, which can be used to derive many other tests. The main methodological finding is that one of the quadratic form methods, which we call a norm approach, emerges as a clear winner in terms of finite-sample performance in nearly every setting we considered. This approach focuses directly on the Frobenius distance between the spatiotemporal covariance function and its separable approximation. We demonstrate the efficacy of our methods via simulations and application to Irish wind data.

Original languageEnglish (US)
Pages (from-to)425-437
Number of pages13
JournalBiometrika
Volume104
Issue number2
DOIs
StatePublished - Jun 1 2017

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Separability
Maximum likelihood
Space-time
Specifications
Monte Carlo Method
Quadratic form
Testing
Asymptotic distribution
Spatio-temporal Data
Functional Data
Covariance Function
Likelihood Methods
testing
Covariance Structure
Frobenius
Joint Distribution
Simulation Methods
Maximum Likelihood Estimator
Monte Carlo method
Efficacy

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Cite this

Constantinou, P. ; Kokoszka, P. ; Reimherr, M. / Testing separability of space-time functional processes. In: Biometrika. 2017 ; Vol. 104, No. 2. pp. 425-437.
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Testing separability of space-time functional processes. / Constantinou, P.; Kokoszka, P.; Reimherr, M.

In: Biometrika, Vol. 104, No. 2, 01.06.2017, p. 425-437.

Research output: Contribution to journalArticle

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