Abstract
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 language | English |
---|---|
Pages (from-to) | 304-326 |
Number of pages | 23 |
Journal | The Canadian Journal of Statistics |
Volume | 50 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2022 |
Keywords
- Functional data
- normality test
- principal components
- spatial statistics
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty