Testing normality of spatially indexed functional data

Siegfried Hörmann, Piotr Kokoszka*, Thomas Kuenzer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This article aims at filling this gap in the case of functional observations on a spatial grid. Our test compares the moments of the spatial (frequency domain) principal component scores to those of a suitable Gaussian distribution. Critical values can be readily obtained from a chi-squared distribution. We provide rigorous theoretical justification for a broad class of weakly stationary functional random fields. We perform simulation studies to assess the power of the test against various alternatives. An application to surface incoming shortwave radiation illustrates the practical value of this procedure.

Original languageEnglish
Pages (from-to)304-326
Number of pages23
JournalThe Canadian Journal of Statistics
Issue number1
Publication statusPublished - Mar 2022


  • Functional data
  • normality test
  • principal components
  • spatial statistics

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Testing normality of spatially indexed functional data'. Together they form a unique fingerprint.

Cite this