Premium
Testing normality of spatially indexed functional data
Author(s) -
Hörmann Siegfried,
Kokoszka Piotr,
Kuenzer Thomas
Publication year - 2022
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11662
Subject(s) - normality , functional data analysis , normality test , statistics , gaussian , functional principal component analysis , principal component analysis , mathematics , computer science , econometrics , statistical hypothesis testing , physics , quantum mechanics
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.