Asymptotics of nonparametric L-1 regression models with dependent data

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

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)1532-1559
Number of pages28
JournalBernoulli
Volume20
Issue number3
DOIs
StatePublished - Aug 2014

All Science Journal Classification (ASJC) codes

  • Statistics and Probability

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