title: Asymptotics of nonparametric L-1 regression models with dependent data.
abstract: We investigate asymptotic properties of least-absolute-deviation or median quantile estimates of the location and scale functions in nonparametric regression models with dependent data from multiple subjects. Under a general dependence structure that allows for longitudinal data and some spatially correlated data, we establish uniform Bahadur representations for the proposed median quantile estimates. The obtained Bahadur representations provide deep insights into the asymptotic behavior of the estimates. Our main theoretical development is based on studying the modulus of continuity of kernel weighted empirical process through a coupling argument. Progesterone data is used for an illustration.
authors: Department of Statistics, Penn State University, University Park, PA 16802.
authors: Zhibiao
authors: Z
authors: Zhao
authors: Department of Biostatistics, Columbia University, 722 West 168th St., New York, NY 10032.
authors: Ying
authors: Y
authors: Wei
authors: Department of Statistics, Penn State University, University Park, PA 16802.
authors: Dennis K J
authors: DK
authors: Lin
keywords: Bahadur representation; Coupling argument; Least-absolute-deviation estimation; Longitudinal data; Nonparametric estimation; Time series; Weighted empirical process