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Distance covariance for random fields. (English) Zbl 1493.62069

Summary: We study an independence test based on distance correlation for random fields \((X, Y)\). We consider the situations when \((X,Y)\) is observed on a lattice with equidistant grid sizes and when \((X, Y)\) is observed at random locations. We provide asymptotic theory for the sample distance correlation in both situations and show bootstrap consistency. The latter fact allows one to build a test for independence of \(X\) and \(Y\) based on the considered discretizations of these fields. We illustrate the performance of the bootstrap test by simulations, and apply the test to Japanese meteorological data observed over the entire area of Japan.

MSC:

62E20 Asymptotic distribution theory in statistics
62G20 Asymptotic properties of nonparametric inference
62M40 Random fields; image analysis
60F05 Central limit and other weak theorems
60F25 \(L^p\)-limit theorems
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