{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,22]],"date-time":"2026-09-22T20:22:26Z","timestamp":1790108546578,"version":"4.0.1"},"reference-count":27,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2003,4,25]],"date-time":"2003-04-25T00:00:00Z","timestamp":1051228800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003,5,1]]},"abstract":"<jats:title>Summary<\/jats:title><jats:p>We show that difference-based methods can be used to construct simple and explicit estimators of error covariance and autoregressive parameters in nonparametric regression with time series errors. When the error process is Gaussian our estimators are efficient, but they are available well beyond the Gaussian case. As an illustration of their usefulness we show that difference-based estimators can be used to produce a simplified version of time series cross-validation. This new approach produces a bandwidth selector that is equivalent, to both first and second orders, to that given by the full time series cross-validation algorithm. Other applications of difference-based methods are to variance estimation and construction of confidence bands in nonparametric regression.<\/jats:p>","DOI":"10.1111\/1467-9868.00395","type":"journal-article","created":{"date-parts":[[2004,12,28]],"date-time":"2004-12-28T19:38:40Z","timestamp":1104262720000},"page":"443-456","source":"Crossref","is-referenced-by-count":56,"title":["Using Difference-Based Methods for Inference in Nonparametric Regression with Time Series Errors"],"prefix":"10.1093","volume":"65","author":[{"given":"Peter","family":"Hall","sequence":"first","affiliation":[{"name":"Australian National University , Canberra , Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ingrid Van","family":"Keilegom","sequence":"additional","affiliation":[{"name":"Australian National University , Canberra , Australia , and , Louvain-la-Neuve , Belgium"},{"name":"Universit\u00e9 catholique de Louvain , Canberra , Australia , and , Louvain-la-Neuve , Belgium"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2003,4,25]]},"reference":[{"key":"2023032908213958100_","volume-title":"The Statistical Analysis of Time Series","author":"Anderson","year":"1971"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"463","DOI":"10.1111\/1467-842X.00099","article-title":"Local linear regression with long-range dependent errors","volume":"41","author":"Anh","year":"1999","journal-title":"Aust. New Z. J. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1017\/S0266466600164011","article-title":"Nonparametric estimation of additive nonlinear ARX time series: local linear fitting and projections","volume":"16","author":"Cai","year":"2000","journal-title":"Econometr. Theory"},{"key":"2023032908213958100_","volume-title":"Local robust regression estimation for time series","author":"Cai","year":"2001"},{"key":"2023032908213958100_","article-title":"Methods for tracking support boundaries with corners","author":"Cheng","year":"2001","journal-title":"Ann. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"1906","DOI":"10.1214\/aos\/1176348377","article-title":"Comparison of two bandwidth selectors with dependent errors","volume":"19","author":"Chu","year":"1991","journal-title":"Ann. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"645","DOI":"10.1093\/biomet\/85.3.645","article-title":"Efficient estimation of conditional variance functions in stochastic regression","volume":"85","author":"Fan","year":"1998","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"1271","DOI":"10.1081\/STA-100104745","article-title":"Local polynomial regression estimation with correlated errors","volume":"30","author":"Francisco-Fernandez","year":"2001","journal-title":"Communs Statist. Theory Meth."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1093\/biomet\/73.3.625","article-title":"Residual variance and residual pattern in nonlinear regression","volume":"73","author":"Gasser","year":"1986","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1093\/biomet\/77.3.521","article-title":"Asymptotically optimal difference-based estimation of variance in nonparametric regression","volume":"77","author":"Hall","year":"1990","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"13345","DOI":"10.1029\/JD092iD11p13345","article-title":"Global trends of measured surface air temperature","volume":"92","author":"Hansen","year":"1987","journal-title":"J. Geophys. Res. D"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1111\/j.1751-5823.1997.tb00367.x","article-title":"A review of nonparametric time series analysis","volume":"65","author":"H\u00e4rdle","year":"1997","journal-title":"Int. Statist. Rev."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1111\/j.2517-6161.1991.tb01816.x","article-title":"Kernel regression estimation with time series errors","volume":"53","author":"Hart","year":"1991","journal-title":"J. R. Statist. Soc. B"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1111\/j.2517-6161.1994.tb01998.x","article-title":"Automated kernel smoothing of dependent data by using time series cross-validation","volume":"56","author":"Hart","year":"1994","journal-title":"J. R. Statist. Soc. B"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"620","DOI":"10.1080\/01621459.1998.10473715","article-title":"One-sided cross-validation.","volume":"93","author":"Hart","year":"1998","journal-title":"J. Am. Statist. Ass."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1093\/biomet\/79.4.783","article-title":"Choice of bandwidth for kernel regression when residuals are correlated","volume":"79","author":"Herrmann","year":"1992","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1111\/j.1467-842X.1997.tb00694.x","article-title":"Nonparametric autocovariance function estimation","volume":"39","author":"Hyndman","year":"1997","journal-title":"Aust. J. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0304-4149(99)00015-0","article-title":"Local linear regression estimation for time series with long-range dependence","volume":"82","author":"Masry","year":"1999","journal-title":"Stoch. Process. Applic."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-3926-0_2","article-title":"Nonparametric regression analysis of longitudinal data","volume":"46","author":"M\u00fcller","year":"1988","journal-title":"Lect. Notes Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"610","DOI":"10.1214\/aos\/1176350364","article-title":"Estimation of heteroscedasticity in regression analysis","volume":"15","author":"M\u00fcller","year":"1987","journal-title":"Ann. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"639","DOI":"10.2307\/2336305","article-title":"Detecting dependencies in smooth regression models","volume":"75","author":"M\u00fcller","year":"1988","journal-title":"Biometrika"},{"key":"2023032908213958100_","first-page":"102","article-title":"Estimating an unknown function by local linear regression when the errors are correlated","author":"Opsomer","year":"1996","journal-title":"Proc. Statist. Comput. Sect. Am. Statist. Ass."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1214\/ss\/1009213287","article-title":"Nonparametric regression with correlated errors","volume":"16","author":"Opsomer","year":"2001","journal-title":"Statist. Sci."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1093\/biomet\/84.4.791","article-title":"Bandwidth selection for kernel regression with long-range dependent errors","volume":"84","author":"Ray","year":"1997","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"1215","DOI":"10.1214\/aos\/1176346788","article-title":"Bandwidth choice for nonparametric regression","volume":"12","author":"Rice","year":"1984","journal-title":"Ann. Statist."},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1093\/biomet\/80.2.373","article-title":"Nonparametric estimation of residual variance revisited","volume":"80","author":"Seifert","year":"1993","journal-title":"Biometrika"},{"key":"2023032908213958100_","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/S0378-3758(97)00151-1","article-title":"Cross-validatory bandwidth selections for regression estimation based on dependent data","volume":"68","author":"Yao","year":"1998","journal-title":"J. Statist. Planng Inf."}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00395","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2F1467-9868.00395","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/2\/443\/49684376\/jrsssb_65_2_443.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/65\/2\/443\/49684376\/jrsssb_65_2_443.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,21]],"date-time":"2024-12-21T21:14:01Z","timestamp":1734815641000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/65\/2\/443\/7092846"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,4,25]]},"references-count":27,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2003,4,25]]},"published-print":{"date-parts":[[2003,5,1]]}},"URL":"https:\/\/doi.org\/10.1111\/1467-9868.00395","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2003,5]]},"published":{"date-parts":[[2003,4,25]]}}}