|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Estimation of fractal dimension for a class of Non-Gaussian stationary processes and fields | | Grace Chan
; Andrew T. A. Wood
; | | Date: |
25 Jun 2004 | | Journal: | Annals of Statistics 2004, Vol. 32, No. 3, 1222-1260 DOI: 10.1214/009053604000000346 | | Subject: | Statistics MSC-class: 62M99 (Primary) 62E20 (Secondary) | math.ST | | Abstract: | We 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 o 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 | | Source: | arXiv, math.ST/0406525 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER