{"title":"基于协方差近似的ml -协方差参数估计的渐近分析","authors":"Reinhard Furrer, Michael Hediger","doi":"10.1214/23-ejs2170","DOIUrl":null,"url":null,"abstract":"Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.","PeriodicalId":49272,"journal":{"name":"Electronic Journal of Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":1.0000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations\",\"authors\":\"Reinhard Furrer, Michael Hediger\",\"doi\":\"10.1214/23-ejs2170\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.\",\"PeriodicalId\":49272,\"journal\":{\"name\":\"Electronic Journal of Statistics\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Electronic Journal of Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/23-ejs2170\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electronic Journal of Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/23-ejs2170","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Asymptotic analysis of ML-covariance parameter estimators based on covariance approximations
Given a zero-mean Gaussian random field with a covariance function that belongs to a parametric family of covariance functions, we introduce a new notion of likelihood approximations, termed truncated-likelihood functions. Truncated-likelihood functions are based on direct functional approximations of the presumed family of covariance functions. For compactly supported covariance functions, within an increasing-domain asymptotic framework, we provide sufficient conditions under which consistency and asymptotic normality of estimators based on truncated-likelihood functions are preserved. We apply our result to the family of generalized Wendland covariance functions and discuss several examples of Wendland approximations. For families of covariance functions that are not compactly supported, we combine our results with the covariance tapering approach and show that ML estimators, based on truncated-tapered likelihood functions, asymptotically minimize the Kullback-Leibler divergence, when the taper range is fixed.
期刊介绍:
The Electronic Journal of Statistics (EJS) publishes research articles and short notes on theoretical, computational and applied statistics. The journal is open access. Articles are refereed and are held to the same standard as articles in other IMS journals. Articles become publicly available shortly after they are accepted.