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Joint asymptotics for estimating the fractal indices of bivariate Gaussian processes. (English) Zbl 1397.62360

Summary: Multivariate (or vector-valued) processes are important for modeling multiple variables. The fractal indices of the components of the underlying multivariate process play a key role in characterizing the dependence structures and statistical properties of the multivariate process. In this paper, under the infill asymptotics framework, we establish joint asymptotic results for the increment-based estimators of bivariate fractal indices. Our main results quantitatively describe the effect of the cross-dependence structure on the performance of the estimators.

MSC:

62M30 Inference from spatial processes
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
62M40 Random fields; image analysis
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