Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields

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dc.creatorChan, Grace
dc.creatorWood, Andrew T. A.
dc.date2004-06-25
dc.date.accessioned2026-07-07T08:06:24Z
dc.date.available2026-07-07T08:06:24Z
dc.descriptionWe present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R\to R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on R^d, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is ``fixed domain'' (or ``infill'') asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat richer than in the Gaussian case (the latter is recovered when g is affine), in part because estimators of the type considered may have an asymptotic variance which is random in the limit. Broadly, when g is smooth and nonaffine, three types of limit distributions can arise, types (i), (ii) and (iii), say. Each type can be represented as a random integral. More specifically, type (i) can be represented as the integral of a certain random function with respect to Lebesgue measure; type (ii) can be represented as the integral of a second random function
dc.identifierhttps://arxiv.org/abs/math/0406525
dc.identifierhttp://arxiv.org/abs/math/0406525
dc.identifierAnnals of Statistics 2004, Vol. 32, No. 3, 1222-1260
dc.identifierdoi:10.1214/009053604000000346
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/130594
dc.subjectStatistics Theory
dc.subject62M99 (Primary) 62E20 (Secondary)
dc.titleEstimation of fractal dimension for a class of Non-Gaussian stationary processes and fields
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