[Statlist] Next talk: Friday, October 28, 2016 with Samantha Leorato Università Tor Vergata, Roma

[Maurer Letizia]

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ETH and University of Zurich

Organisers:
Proff. P. Bühlmann - L. Held - T. Hothorn - M. Maathuis - N. Meinshausen - S. van de Geer - M. Wolf

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We are glad to announce the following talk:

Friday, October 28, 2016 at 15.15h  ETH Zurich HG G19.1G E 41
with Samantha Leorato Università Tor Vergata, Roma

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Title:

Distribution and Quantile Regressions <https://www.math.ethz.ch/sfs/news-and-events/research-seminar.html?s=hs16#e_8707>

Abstract:

Given a continuous random variable Y and a random vector X defined on the same probability space, the conditional distribution function (CDF) and the conditional quantile function (CQF) give rise to two competing approaches to the estimation of the conditional distribution of Y given X. One approach -- distribution regression -- is based on direct estimation of the conditional distribution function (CDF); the other approach -- quantile regression -- is instead based on direct estimation of the conditional quantile function (CQF). Since the CDF and the CQF are generalized inverses of each other, estimates of any functional of the distribution may be obtained by appropriately transforming the direct estimates of the CDF and the CQ. Similarly, indirect estimates of the CQF and the CDF may be obtained by taking the generalized inverse of the direct estimates. Contrary to the QR estimator, that typically refers to a conditional ALAD estimator, there is no unique choice for the DR estimator. One possibility is to define a binary choice model for any given threshold $y$ and the corresponding dummy variable $\{Y\leq y\}$. This choice is particularly suited to comparisons with the QR estimator, since, in the unconditional case, the two approaches are equivalent. Our paper focuses on comparing QR and DR approaches, and their performances in terms of efficiency, both asymptotically and for finite samples. Asymptotic efficiency is measured by asymptotic MSE of the rescaled estimators of the CDF (or of the CQF), where asymptotic MSE is the sum of the asymptotic variance and of the squared asymptotic bias. Asymptotic bias is allowed to be nonzero, thus taking into account some form of \emph{local} misspecification of either the QR or the DR models. For the asymptotic variance, we show that the choice of the link function used for DR estimation matters, and that under the most popular error distributions (i.e. logistic and normal) the QR is uniformly more efficient (in expectation). The finite sample performance is assessed by an extensive Monte Carlo exercise.

This abstract is also to be found under the following link: http://stat.ethz.ch/events/research_seminar

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