{"title":"Inference for Seemingly Unrelated Varying-Coefficient Nonparametric Regression Models.","authors":"Jinhong You, Haibo Zhou","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>This paper is concerned with the inference of seemingly unrelated (SU) varying-coefficient nonparametric regression models. We propose an estimation for the unknown coefficient functions, which is an extension of the two-stage procedure proposed by Linton, <i>et al.</i> (2004) in the longitudinal data framework where they focused on purely nonparametric regression. We show the resulted estimators are asymptotically normal and more efficient than those based on only the individual regression equation even when the error covariance matrix is homogeneous. Another focus of this paper is to extend the generalized likelihood ratio technique developed by Fan, Zhang and Zhang (2001) for testing the goodness of fit of models to the setting of SU regression. A wild block bootstrap based method is used to compute <i>p</i>-value of the test. Some simulation studies are given in support of the asymptotics. A real data set from an ongoing environmental epidemiologic study is used to illustrate the proposed procedures.</p>","PeriodicalId":89573,"journal":{"name":"International journal of statistics and management system","volume":"5 1-2","pages":"59-83"},"PeriodicalIF":0.0,"publicationDate":"2010-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3893667/pdf/nihms329684.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"32052807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Statistical Inference for Regression Models with Covariate Measurement Error and Auxiliary Information.","authors":"Jinhong You, Haibo Zhou","doi":"","DOIUrl":"","url":null,"abstract":"<p><p>We consider statistical inference on a regression model in which some covariables are measured with errors together with an auxiliary variable. The proposed estimation for the regression coefficients is based on some estimating equations. This new method alleates some drawbacks of previously proposed estimations. This includes the requirment of undersmoothing the regressor functions over the auxiliary variable, the restriction on other covariables which can be observed exactly, among others. The large sample properties of the proposed estimator are established. We further propose a jackknife estimation, which consists of deleting one estimating equation (instead of one obervation) at a time. We show that the jackknife estimator of the regression coefficients and the estimating equations based estimator are asymptotically equivalent. Simulations show that the jackknife estimator has smaller biases when sample size is small or moderate. In addition, the jackknife estimation can also provide a consistent estimator of the asymptotic covariance matrix, which is robust to the heteroscedasticity. We illustrate these methods by applying them to a real data set from marketing science.</p>","PeriodicalId":89573,"journal":{"name":"International journal of statistics and management system","volume":"4 1-2","pages":"96-12"},"PeriodicalIF":0.0,"publicationDate":"2009-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3244303/pdf/nihms329678.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"30349087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}