A0360
Title: Simultaneous confidence bands for partially linear single-index models for longitudinal data
Authors: Li Cai - Zhejiang Gongshang University (China)
Lei Jin - Texas A and M University at Corpus Christi (United States)
Suojin Wang - Texas A and M University (United States) [presenting]
Abstract: An asymptotically accurate simultaneous confidence band (SCB) is proposed for the nonparametric link function in the partially linear single-index models for longitudinal data under general conditions including both unbalanced and non normal cases. To formulate such a band, a two-step semiparametric estimation method combing local linear smoothing and generalized estimating equations is adopted to estimate both the link function and the parametric components. The estimator for the link function is shown to be oracally efficient, in the sense that it is asymptotically equivalent to that with all true values of the parameters being known oracally. Furthermore, using the oracle efficiency the asymptotic distribution of the maximal deviation of the two-step estimator is provided, and hence an SCB for the link function is constructed. Finite-sample simulation studies are carried out which support our asymptotic theory. The proposed SCB is applied to a CD4 data set to analyze and test the trend of the CD4 cell numbers.
