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Testing Gaussianity and Linearity For Random Fields in the Frequency Domain
Author(s) -
Yuan J.
Publication year - 2000
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/1467-9892.00207
Subject(s) - mathematics , linearity , spectrum (functional analysis) , asymptotic distribution , series (stratigraphy) , statistics , statistical physics , mathematical analysis , physics , quantum mechanics , paleontology , estimator , biology
We consider tests of Gaussianity and linearity for random fields on Z d , where Z is the set of integers and d ≥ 1. As in the time series case, the idea is to test the constancy (zero or otherwise) of the modulus of the k th‐order normalized spectrum ( k > 2). We derive the asymptotic normality of the real part, the imaginary part and the modulus of the estimated normalized k th‐order spectrum at fixed frequencies. This leads to the formation of likelihood‐ratio tests. The test statistics are simple and intuitively plausible, and their asymptotic distributions are given in terms of deviations from Gaussianity and linearity.