Asymptotics of nonparametric L-1 regression models with dependent data

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 c...

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Published inBernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability Vol. 20; no. 3; p. 1532
Main Authors Zhao, Zhibiao, Wei, Ying, Lin, Dennis K J
Format Journal Article
LanguageEnglish
Published England 01.08.2014
Subjects
Coupling argument
Time series
Weighted empirical process
Nonparametric estimation
Bahadur representation
Longitudinal data
Least-absolute-deviation estimation
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Summary: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.
ISSN:1350-7265
DOI:10.3150/13-BEJ532