Matches in SemOpenAlex for { <https://semopenalex.org/work/W4285704454> ?p ?o ?g. }
Showing items 1 to 48 of
48
with 100 items per page.
- W4285704454 abstract "Optimal linear prediction (aka. kriging) of a random field ${Z(x)}_{xinmathcal{X}}$ indexed by a compact metric space $(mathcal{X},d_{mathcal{X}})$ can be obtained if the mean value function $mcolonmathcal{X}tomathbb{R}$ and the covariance function $varrhocolonmathcal{X}timesmathcal{X}tomathbb{R}$ of $Z$ are known. We consider the problem of predicting the value of $Z(x^*)$ at some location $x^*inmathcal{X}$ based on observations at locations ${x_j}_{j=1}^n$ which accumulate at $x^*$ as $ntoinfty$ (or, more generally, predicting $varphi(Z)$ based on ${varphi_j(Z)}_{j=1}^n$ for linear functionals $varphi,varphi_1,ldots,varphi_n$). Our main result characterizes the asymptotic performance of linear predictors (as $n$ increases) based on an incorrect second order structure $(tilde{m},tilde{varrho})$, without any restrictive assumptions on $varrho,tilde{varrho}$ such as stationarity. We, for the first time, provide necessary and sufficient conditions on $(tilde{m},tilde{varrho})$ for asymptotic optimality of the corresponding linear predictor holding uniformly with respect to $varphi$. These general results are illustrated by weakly stationary random fields on $mathcal{X}subsetmathbb{R}^d$ with Mat'ern or periodic covariance functions, and on the sphere $mathcal{X}=mathbb{S}^2$ for the case of two isotropic covariance functions." @default.
- W4285704454 created "2022-07-18" @default.
- W4285704454 creator A5001017767 @default.
- W4285704454 creator A5040844010 @default.
- W4285704454 date "2020-05-18" @default.
- W4285704454 modified "2023-09-27" @default.
- W4285704454 title "Necessary and sufficient conditions for asymptotically optimal linear prediction of random fields on compact metric spaces" @default.
- W4285704454 doi "https://doi.org/10.48550/arxiv.2005.08904" @default.
- W4285704454 hasPublicationYear "2020" @default.
- W4285704454 type Work @default.
- W4285704454 citedByCount "0" @default.
- W4285704454 crossrefType "posted-content" @default.
- W4285704454 hasAuthorship W4285704454A5001017767 @default.
- W4285704454 hasAuthorship W4285704454A5040844010 @default.
- W4285704454 hasBestOaLocation W42857044541 @default.
- W4285704454 hasConcept C105795698 @default.
- W4285704454 hasConcept C114614502 @default.
- W4285704454 hasConcept C138885662 @default.
- W4285704454 hasConcept C176370821 @default.
- W4285704454 hasConcept C178650346 @default.
- W4285704454 hasConcept C2778572836 @default.
- W4285704454 hasConcept C33923547 @default.
- W4285704454 hasConcept C41895202 @default.
- W4285704454 hasConceptScore W4285704454C105795698 @default.
- W4285704454 hasConceptScore W4285704454C114614502 @default.
- W4285704454 hasConceptScore W4285704454C138885662 @default.
- W4285704454 hasConceptScore W4285704454C176370821 @default.
- W4285704454 hasConceptScore W4285704454C178650346 @default.
- W4285704454 hasConceptScore W4285704454C2778572836 @default.
- W4285704454 hasConceptScore W4285704454C33923547 @default.
- W4285704454 hasConceptScore W4285704454C41895202 @default.
- W4285704454 hasLocation W42857044541 @default.
- W4285704454 hasLocation W42857044542 @default.
- W4285704454 hasOpenAccess W4285704454 @default.
- W4285704454 hasPrimaryLocation W42857044541 @default.
- W4285704454 hasRelatedWork W1681512102 @default.
- W4285704454 hasRelatedWork W1978042415 @default.
- W4285704454 hasRelatedWork W2005988940 @default.
- W4285704454 hasRelatedWork W2017331178 @default.
- W4285704454 hasRelatedWork W2024105718 @default.
- W4285704454 hasRelatedWork W2260035625 @default.
- W4285704454 hasRelatedWork W2918266370 @default.
- W4285704454 hasRelatedWork W2976797620 @default.
- W4285704454 hasRelatedWork W2997711642 @default.
- W4285704454 hasRelatedWork W3086542228 @default.
- W4285704454 isParatext "false" @default.
- W4285704454 isRetracted "false" @default.
- W4285704454 workType "article" @default.