Matches in SemOpenAlex for { <https://semopenalex.org/work/W3098179269> ?p ?o ?g. }
Showing items 1 to 88 of
88
with 100 items per page.
- W3098179269 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→R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on Rd, 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 with respect to an independent Gaussian random measure; and type (iii) can be represented as a Wiener–Itô integral of order 2. Which type occurs depends on a combination of the following factors: the roughness of X(t), whether d=1 or d=2 and the order of the increment which is used. Another notable feature of our results is that, even though the estimators we consider are based on a variogram, no moment conditions are required on the observed field g{X(t)} for the limit theory to hold. The results of a numerical study are also presented." @default.
- W3098179269 created "2020-11-23" @default.
- W3098179269 creator A5017122202 @default.
- W3098179269 creator A5019248593 @default.
- W3098179269 date "2004-06-01" @default.
- W3098179269 modified "2023-10-14" @default.
- W3098179269 title "Estimation of fractal dimension for a class of non-Gaussian stationary processes and fields" @default.
- W3098179269 cites W1964702866 @default.
- W3098179269 cites W1967924750 @default.
- W3098179269 cites W1970669268 @default.
- W3098179269 cites W1976759018 @default.
- W3098179269 cites W1990795692 @default.
- W3098179269 cites W1997442068 @default.
- W3098179269 cites W2010176447 @default.
- W3098179269 cites W2017769677 @default.
- W3098179269 cites W2023575643 @default.
- W3098179269 cites W2051317301 @default.
- W3098179269 cites W2067991671 @default.
- W3098179269 cites W2100676242 @default.
- W3098179269 cites W2113161618 @default.
- W3098179269 cites W2527389923 @default.
- W3098179269 cites W4247047207 @default.
- W3098179269 cites W4293510232 @default.
- W3098179269 cites W55912154 @default.
- W3098179269 doi "https://doi.org/10.1214/009053604000000346" @default.
- W3098179269 hasPublicationYear "2004" @default.
- W3098179269 type Work @default.
- W3098179269 sameAs 3098179269 @default.
- W3098179269 citedByCount "26" @default.
- W3098179269 countsByYear W30981792692012 @default.
- W3098179269 countsByYear W30981792692013 @default.
- W3098179269 countsByYear W30981792692014 @default.
- W3098179269 countsByYear W30981792692015 @default.
- W3098179269 countsByYear W30981792692017 @default.
- W3098179269 countsByYear W30981792692018 @default.
- W3098179269 countsByYear W30981792692020 @default.
- W3098179269 countsByYear W30981792692021 @default.
- W3098179269 countsByYear W30981792692022 @default.
- W3098179269 crossrefType "journal-article" @default.
- W3098179269 hasAuthorship W3098179269A5017122202 @default.
- W3098179269 hasAuthorship W3098179269A5019248593 @default.
- W3098179269 hasBestOaLocation W30981792691 @default.
- W3098179269 hasConcept C105795698 @default.
- W3098179269 hasConcept C121332964 @default.
- W3098179269 hasConcept C130402806 @default.
- W3098179269 hasConcept C134306372 @default.
- W3098179269 hasConcept C137250428 @default.
- W3098179269 hasConcept C163716315 @default.
- W3098179269 hasConcept C166785042 @default.
- W3098179269 hasConcept C178650346 @default.
- W3098179269 hasConcept C185429906 @default.
- W3098179269 hasConcept C33923547 @default.
- W3098179269 hasConcept C51267290 @default.
- W3098179269 hasConcept C61326573 @default.
- W3098179269 hasConcept C62520636 @default.
- W3098179269 hasConceptScore W3098179269C105795698 @default.
- W3098179269 hasConceptScore W3098179269C121332964 @default.
- W3098179269 hasConceptScore W3098179269C130402806 @default.
- W3098179269 hasConceptScore W3098179269C134306372 @default.
- W3098179269 hasConceptScore W3098179269C137250428 @default.
- W3098179269 hasConceptScore W3098179269C163716315 @default.
- W3098179269 hasConceptScore W3098179269C166785042 @default.
- W3098179269 hasConceptScore W3098179269C178650346 @default.
- W3098179269 hasConceptScore W3098179269C185429906 @default.
- W3098179269 hasConceptScore W3098179269C33923547 @default.
- W3098179269 hasConceptScore W3098179269C51267290 @default.
- W3098179269 hasConceptScore W3098179269C61326573 @default.
- W3098179269 hasConceptScore W3098179269C62520636 @default.
- W3098179269 hasIssue "3" @default.
- W3098179269 hasLocation W30981792691 @default.
- W3098179269 hasLocation W30981792692 @default.
- W3098179269 hasOpenAccess W3098179269 @default.
- W3098179269 hasPrimaryLocation W30981792691 @default.
- W3098179269 hasRelatedWork W1541863749 @default.
- W3098179269 hasRelatedWork W2069407179 @default.
- W3098179269 hasRelatedWork W2138958818 @default.
- W3098179269 hasRelatedWork W2599475653 @default.
- W3098179269 hasRelatedWork W3002473118 @default.
- W3098179269 hasRelatedWork W3103935687 @default.
- W3098179269 hasRelatedWork W4226291750 @default.
- W3098179269 hasRelatedWork W4286883315 @default.
- W3098179269 hasRelatedWork W4289785401 @default.
- W3098179269 hasRelatedWork W4380083022 @default.
- W3098179269 hasVolume "32" @default.
- W3098179269 isParatext "false" @default.
- W3098179269 isRetracted "false" @default.
- W3098179269 magId "3098179269" @default.
- W3098179269 workType "article" @default.