## Annals of Statistics

### Quantile regression with varying coefficients

Mi-Ok Kim

#### Abstract

Quantile regression provides a framework for modeling statistical quantities of interest other than the conditional mean. The regression methodology is well developed for linear models, but less so for nonparametric models. We consider conditional quantiles with varying coefficients and propose a methodology for their estimation and assessment using polynomial splines. The proposed estimators are easy to compute via standard quantile regression algorithms and a stepwise knot selection algorithm. The proposed Rao-score-type test that assesses the model against a linear model is also easy to implement. We provide asymptotic results on the convergence of the estimators and the null distribution of the test statistic. Empirical results are also provided, including an application of the methodology to forced expiratory volume (FEV) data.

#### Article information

Source
Ann. Statist., Volume 35, Number 1 (2007), 92-108.

Dates
First available in Project Euclid: 6 June 2007

https://projecteuclid.org/euclid.aos/1181100182

Digital Object Identifier
doi:10.1214/009053606000000966

Mathematical Reviews number (MathSciNet)
MR2332270

Zentralblatt MATH identifier
1114.62051

Subjects
Primary: 62G08: Nonparametric regression 62G35: Robustness

#### Citation

Kim, Mi-Ok. Quantile regression with varying coefficients. Ann. Statist. 35 (2007), no. 1, 92--108. doi:10.1214/009053606000000966. https://projecteuclid.org/euclid.aos/1181100182

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