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February 2019 Nonparametric depth and quantile regression for functional data
Joydeep Chowdhury, Probal Chaudhuri
Bernoulli 25(1): 395-423 (February 2019). DOI: 10.3150/17-BEJ991


We investigate nonparametric regression methods based on spatial depth and quantiles when the response and the covariate are both functions. As in classical quantile regression for finite dimensional data, regression techniques developed here provide insight into the influence of the functional covariate on different parts, like the center as well as the tails, of the conditional distribution of the functional response. Depth and quantile based nonparametric regression methods are useful to detect heteroscedasticity in functional regression. We derive the asymptotic behavior of the nonparametric depth and quantile regression estimates, which depend on the small ball probabilities in the covariate space. Our nonparametric regression procedures are used to analyze a dataset about the influence of per capita GDP on saving rates for 125 countries, and another dataset on the effects of per capita net disposable income on the sale of cigarettes in some states in the US.


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Joydeep Chowdhury. Probal Chaudhuri. "Nonparametric depth and quantile regression for functional data." Bernoulli 25 (1) 395 - 423, February 2019.


Received: 1 June 2016; Revised: 1 September 2017; Published: February 2019
First available in Project Euclid: 12 December 2018

zbMATH: 07007212
MathSciNet: MR3892324
Digital Object Identifier: 10.3150/17-BEJ991

Keywords: Bahadur representation , conditional spread , Convergence rates , maximal depth set , spatial depth , spatial quantile

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability


Vol.25 • No. 1 • February 2019
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