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Zhao Z, Wei Y, Lin DK. Asymptotics of nonparametric L-1 regression models with dependent data. Bernoulli (Andover). 2014;20(3):1532-1559doi: 10.3150/13-BEJ532.
Zhao, Z., Wei, Y., & Lin, D. K. (2014). Asymptotics of nonparametric L-1 regression models with dependent data. Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability, 20(3), 1532-1559. https://doi.org/10.3150/13-BEJ532
Zhao, Zhibiao, et al. "Asymptotics of nonparametric L-1 regression models with dependent data." Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability vol. 20,3 (2014): 1532-1559. doi: https://doi.org/10.3150/13-BEJ532
Zhao Z, Wei Y, Lin DK. Asymptotics of nonparametric L-1 regression models with dependent data. Bernoulli (Andover). 2014 Aug 01;20(3):1532-1559. doi: 10.3150/13-BEJ532. PMID: 24955016; PMCID: PMC4060752.
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Bernoulli (Andover). 2014 Aug 01;20(3):1532-1559. doi: 10.3150/13-BEJ532.

Asymptotics of nonparametric L-1 regression models with dependent data.

Bernoulli : official journal of the Bernoulli Society for Mathematical Statistics and Probability

Zhibiao Zhao, Ying Wei, Dennis K J Lin

Affiliations

  1. Department of Statistics, Penn State University, University Park, PA 16802.
  2. Department of Biostatistics, Columbia University, 722 West 168th St., New York, NY 10032.

PMID: 24955016 PMCID: PMC4060752 DOI: 10.3150/13-BEJ532

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.

Keywords: Bahadur representation; Coupling argument; Least-absolute-deviation estimation; Longitudinal data; Nonparametric estimation; Time series; Weighted empirical process

References

  1. Stat Med. 2003 Dec 15;22(23):3655-69 - PubMed
  2. Proc Natl Acad Sci U S A. 2005 Oct 4;102(40):14150-4 - PubMed
  3. Ann Appl Stat. 2012 Mar 1;6(1):409-427 - PubMed

Publication Types

Grant support