2019
DOI: 10.3150/17-bej991
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Nonparametric depth and quantile regression for functional data

Abstract: 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 heteroscedas… Show more

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Cited by 24 publications
(14 citation statements)
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“…For the bivariate curves in the third row of Figure 10 Additional Applications Two applications on more generally structured functional data are demonstrated: the Cigarette data (Chowdhury and Chaudhuri, 2016) are four-dimensional functional data recorded on a one-dimensional time interval; image data from a video filmed by a static camera are three-dimensional functional data recorded on a two-dimensional space.…”
Section: Ms−plotmentioning
confidence: 99%
“…For the bivariate curves in the third row of Figure 10 Additional Applications Two applications on more generally structured functional data are demonstrated: the Cigarette data (Chowdhury and Chaudhuri, 2016) are four-dimensional functional data recorded on a one-dimensional time interval; image data from a video filmed by a static camera are three-dimensional functional data recorded on a two-dimensional space.…”
Section: Ms−plotmentioning
confidence: 99%
“…The success of spatial quantiles is partly explained by their ability to cope with high-dimensional data and even functional data; see, e.g., [3], [4], [5] and [6]. These quantiles were also used with much success to conduct multiple-output quantile regression, again also in the framework of functional data analysis; we refer to [7], [9], and [10]. The present work, however, focuses on the finite-dimensional case.…”
Section: Introductionmentioning
confidence: 99%
“…Delicado and Vieu, 2017). In the one-dimensional case that we consider here, it is well known that the Wasserstein transport can also be expressed in terms of quantile functions (Hoeffding, 1940;Zhang and Müller, 2011;Chowdhury and Chaudhuri, 2019).…”
Section: Introductionmentioning
confidence: 99%