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Asymptotic normality of DHD estimators in a partially linear model
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The paper studies a partially linear regression model given by $$\begin{aligned} y_i=x_i^T\beta +f(t_i)+\varepsilon _i,i=1,2,\ldots ,n, \end{aligned}$$where \(\{\varepsilon _i,i=1,2,\ldots , n\}\) are independent and identically distributed random errors with zero mean and finite variance \(\sigma ^2>0\). Using a difference based and the Huber–Dutter (DHD) approaches, the estimators of unknown parametric component \(\beta \) and root variance \(\sigma \) are given, and then the estimation of nonparametric component \(f(\cdot )\) is given by the wavelet method. The asymptotic normality of the DHD estimators of \(\beta \) and \(\sigma \) are investigated, and the weak convergence rate of the estimator of \(f(\cdot )\) is also investigated. In addition, for stationary \(m\)-dependent sequence of random variables, the central limit theorem is also obtained. At last, two examples are presented to illustrate the proposed method.KeywordsPartially linear regression modelDifference-based method Huber–Dutter estimatorAsymptotic normalityWeak convergence rateMathematics Subject Classification62G0562G20ReferencesAntoniads A, Gregoire G, Mckeague IW (1994) Wavelet methods for cure estimation. J Am Stat Assoc 89:1340–1353CrossRefMATHGoogle ScholarArashi M, Roozbeh M, Niroumand HA (2012) A note on Stein-type shrinkage estimator in partial linearmodels. Statistics 46(5):673–685MathSciNetCrossRefMATHGoogle ScholarArashi M, Valizadeh T (2015) Performance of Kibrias methods in partial linear ridge regression model. Stat Pap 56:231–246MathSciNetCrossRefMATHGoogle ScholarBianco A, Boente G (2004) Robust estimators in semiparametric partly linear regression models. J Stat Plan Inference 122:229–252MathSciNetCrossRefMATHGoogle ScholarBianco A, Boente G, Martinez E (2006) Robust tests in semiparametric partly linear regression models. 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J Multivar Anal 122:251–270MathSciNetCrossRefMATHGoogle ScholarCopyright information© Springer-Verlag Berlin Heidelberg 2015Authors and AffiliationsHongchang Hu1Email authorYu Zhang1Xiong Pan21.School of Mathematics and StatisticsHubei Normal UniversityHuangshiChina2.Faculty of Information EngineeringChina University GeosciencesWuhanChina About this article CrossMark Print ISSN 0932-5026 Online ISSN 1613-9798 Publisher Name Springer Berlin Heidelberg About this journal Reprints and Permissions Article actions function trackAddToCart() { var buyBoxPixel = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox", product: "10.1007/s00362-015-0666-2_Asymptotic normality of DHD estima", productStatus: "add", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); buyBoxPixel.sendinfo(); } function trackSubscription() { var subscription = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "springer_com.buybox" }); subscription.sendinfo({linkId: "inst. subscription info"}); } window.addEventListener("load", function(event) { var viewPage = new webtrekkV3({ trackDomain: "springergmbh01.webtrekk.net", trackId: "196033507532344", domain: "link.springer.com", contentId: "SL-article", product: "10.1007/s00362-015-0666-2_Asymptotic normality of DHD estima", productStatus: "view", productCategory : { 1 : "ppv" }, customEcommerceParameter : { 9 : "link.springer.com" } }); viewPage.sendinfo(); }); Log in to check your access to this article Buy (PDF)EUR 34,95 Unlimited access to full article Instant download (PDF) Price includes local sales tax if applicable Find out about institutional subscriptions Export citation .RIS Papers Reference Manager RefWorks Zotero .ENW EndNote .BIB BibTeX JabRef Mendeley Share article Email Facebook Twitter LinkedIn Cookies We use cookies to improve your experience with our site. 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