Bernoulli

  • Bernoulli
  • Volume 20, Number 3 (2014), 1532-1559.

Asymptotics of nonparametric L-1 regression models with dependent data

Zhibiao Zhao, Ying Wei, and Dennis K.J. Lin

Full-text: Open access

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.

Article information

Source
Bernoulli, Volume 20, Number 3 (2014), 1532-1559.

Dates
First available in Project Euclid: 11 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.bj/1402488949

Digital Object Identifier
doi:10.3150/13-BEJ532

Mathematical Reviews number (MathSciNet)
MR3217453

Zentralblatt MATH identifier
06327918

Keywords
Bahadur representation coupling argument least-absolute-deviation estimation longitudinal data nonparametric estimation time series weighted empirical process

Citation

Zhao, Zhibiao; Wei, Ying; Lin, Dennis K.J. Asymptotics of nonparametric L-1 regression models with dependent data. Bernoulli 20 (2014), no. 3, 1532--1559. doi:10.3150/13-BEJ532. https://projecteuclid.org/euclid.bj/1402488949


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