tailieunhanh - Báo cáo hóa học: " Strong consistency of estimators in partially linear models for longitudinal data with mixingdependent structure"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Strong consistency of estimators in partially linear models for longitudinal data with mixingdependent structure | Zhou and Lin Journal of Inequalities and Applications 2011 2011 112 http content 2011 1 112 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Strong consistency of estimators in partially linear models for longitudinal data with mixingdependent structure Xing-cai Zhou1 2 and Jin-guan Lin 1 Correspondence jglin@ department of Mathematics Southeast University Nanjing 210096 People s Republic of China Full list of author information is available at the end of the article Springer Abstract For exhibiting dependence among the observations within the same subject the paper considers the estimation problems of partially linear models for longitudinal data with the -mixing and p-mixing error structures respectively. The strong consistency for least squares estimator of parametric component is studied. In addition the strong consistency and uniform consistency for the estimator of nonparametric function are investigated under some mild conditions. Keywords partially linear model longitudinal data mixing dependent strong consistency 1 Introduction Longitudinal data Diggle et al. 1 are characterized by repeated observations over time on the same set of individuals. They are common in medical and epidemiological studies. Examples of such data can be easily found in clinical trials and follow-up studies for monitoring disease progression. Interest of the study is often focused on evaluating the effects of time and covariates on the outcome variables. Let tj be the time of the jth measurement of the ith subject Xj e Rp and yy be the ith subject s observed covariate and outcome at time tij respectively. We assume that the full dataset Xy yij ty i 1 . n j 1 . mJ where n is the number of subjects and mi is the number of repeated measurements of the ith subject is observed and can be modeled as the following partially linear models Ỵij Xij p g tij eij where b is a p X 1 vector of unknown .