A regression approach for estimating the parameters of the covariance function of a stationary spatial random process
Saved in:
| Title: | A regression approach for estimating the parameters of the covariance function of a stationary spatial random process |
|---|---|
| Authors: | Hyun, Jung Won jwhyun@ucdavis.edu, Burman, Prabir1, Paul, Debashis1 |
| Source: | Journal of Statistical Planning & Inference. Aug2012, Vol. 142 Issue 8, p2330-2344. 15p. |
| Subjects: | Parameter estimation, Analysis of covariance, Stochastic processes, Regression analysis, Maximum likelihood statistics, Statistical correlation |
| Abstract: | Abstract: We consider the problem of estimating the parameters of the covariance function of a stationary spatial random process. In spatial statistics, there are widely used parametric forms for the covariance functions, and various methods for estimating the parameters have been proposed in the literature. We develop a method for estimating the parameters of the covariance function that is based on a regression approach. Our method utilizes pairs of observations whose distances are closest to a value which is chosen in a way that the estimated correlation at distance h is a predetermined value. We demonstrate the effectiveness of our procedure by simulation studies and an application to a water pH data set. Simulation studies show that our method outperforms all well-known least squares-based approaches to the variogram estimation and is comparable to the maximum likelihood estimation of the parameters of the covariance function. We also show that under a mixing condition on the random field, the proposed estimator is consistent for standard one parameter models for stationary correlation functions. [Copyright &y& Elsevier] |
| Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 74308675 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: A regression approach for estimating the parameters of the covariance function of a stationary spatial random process – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Hyun%2C+Jung+Won%22">Hyun, Jung Won</searchLink><i> jwhyun@ucdavis.edu</i><br /><searchLink fieldCode="AR" term="%22Burman%2C+Prabir%22">Burman, Prabir</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Paul%2C+Debashis%22">Paul, Debashis</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Statistical+Planning+%26+Inference%22">Journal of Statistical Planning & Inference</searchLink>. Aug2012, Vol. 142 Issue 8, p2330-2344. 15p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Parameter+estimation%22">Parameter estimation</searchLink><br /><searchLink fieldCode="DE" term="%22Analysis+of+covariance%22">Analysis of covariance</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+processes%22">Stochastic processes</searchLink><br /><searchLink fieldCode="DE" term="%22Regression+analysis%22">Regression analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Maximum+likelihood+statistics%22">Maximum likelihood statistics</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: We consider the problem of estimating the parameters of the covariance function of a stationary spatial random process. In spatial statistics, there are widely used parametric forms for the covariance functions, and various methods for estimating the parameters have been proposed in the literature. We develop a method for estimating the parameters of the covariance function that is based on a regression approach. Our method utilizes pairs of observations whose distances are closest to a value which is chosen in a way that the estimated correlation at distance h is a predetermined value. We demonstrate the effectiveness of our procedure by simulation studies and an application to a water pH data set. Simulation studies show that our method outperforms all well-known least squares-based approaches to the variogram estimation and is comparable to the maximum likelihood estimation of the parameters of the covariance function. We also show that under a mixing condition on the random field, the proposed estimator is consistent for standard one parameter models for stationary correlation functions. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Statistical Planning & Inference is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=74308675 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jspi.2012.03.005 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 2330 Subjects: – SubjectFull: Parameter estimation Type: general – SubjectFull: Analysis of covariance Type: general – SubjectFull: Stochastic processes Type: general – SubjectFull: Regression analysis Type: general – SubjectFull: Maximum likelihood statistics Type: general – SubjectFull: Statistical correlation Type: general Titles: – TitleFull: A regression approach for estimating the parameters of the covariance function of a stationary spatial random process Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Hyun, Jung Won – PersonEntity: Name: NameFull: Burman, Prabir – PersonEntity: Name: NameFull: Paul, Debashis IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2012 Type: published Y: 2012 Identifiers: – Type: issn-print Value: 03783758 Numbering: – Type: volume Value: 142 – Type: issue Value: 8 Titles: – TitleFull: Journal of Statistical Planning & Inference Type: main |
| ResultId | 1 |
