Zhao Zhibiao, Wei Ying, Lin Dennis K J
Department of Statistics, Penn State University, University Park, PA 16802.
Department of Biostatistics, Columbia University, 722 West 168th St., New York, NY 10032.
Bernoulli (Andover). 2014 Aug 1;20(3):1532-1559. doi: 10.3150/13-BEJ532.
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.
我们研究了来自多个受试者的相关数据的非参数回归模型中位置和尺度函数的最小绝对偏差或中位数分位数估计的渐近性质。在允许纵向数据和一些空间相关数据的一般相依结构下，我们为所提出的中位数分位数估计建立了一致的Bahadur表示。所得到的Bahadur表示为估计的渐近行为提供了深刻的见解。我们主要的理论发展是基于通过耦合论证研究核加权经验过程的连续性模。以孕酮数据为例进行说明。
