Distance covariance for random fields

2021/07/07 by Muneya Matsui, Matsui, Muneya, Thomas Mikosch +5
Decision Sciences · Economics, Econometrics and Finance · #FOS: Mathematics #Financial Risk and Volatility Modeling #Primary 62E20 #Probability and Risk Models #Secondary 62G20 62M99 60F05 60F25 #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2107.03162

openalex publication_date 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 in a simulation study involving fractional Brownian and infinite variance stable fields. The independence test is applied to Japanese meteorological data, which are observed over the entire area of Japan.

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