Distributional vs. Quantile Regression

45 Pages Posted: 17 Dec 2013

See all articles by Roger Koenker

Roger Koenker

University of Illinois at Urbana-Champaign - Department of Economics

Samantha Leorato

Dep. Economics Management and Quantitative Methods

Franco Peracchi

University of Rome Tor Vergata - Department of Economics and Finance; Einaudi Institute for Economics and Finance (EIEF)

Date Written: December 17, 2013

Abstract

Given a scalar random variable Y and a random vector X defined on the same probability space, the conditional distribution of Y given X can be represented by either the conditional distribution function or the conditional quantile function. To these equivalent representations correspond two alternative approaches to estimation. One approach, distributional regression (DR), is based on direct estimation of the conditional distribution function; the other approach, quantile regression (QR), is instead based on direct estimation of the conditional quantile function. Indirect estimates of the conditional quantile function and the conditional distribution function may then be obtained by inverting the direct estimates obtained from either approach. Despite the growing attention to the DR approach, and the vast literature on the QR approach, the link between the two approaches has not been explored in detail. The aim of this paper is to fill-in this gap by providing a better understanding of the relative performance of the two approaches, both asymptotically and in finite samples, under the linear location model and certain types of heteroskedastic location-scale models.

Keywords: Quantile regression, distributional regression, functional Delta-method, asymptotic relative efficiency, linear location model, location-scale models

JEL Classification: C1, C21, C25

Suggested Citation

Koenker, Roger W. and Leorato, Samantha and Peracchi, Franco, Distributional vs. Quantile Regression (December 17, 2013). CEIS Working Paper No. 300, Available at SSRN: https://ssrn.com/abstract=2368737 or http://dx.doi.org/10.2139/ssrn.2368737

Roger W. Koenker

University of Illinois at Urbana-Champaign - Department of Economics ( email )

410 David Kinley Hall
1407 W. Gregory
Urbana, IL 61801
United States
217-333-4558 (Phone)
217-244-6571 (Fax)

Samantha Leorato

Dep. Economics Management and Quantitative Methods ( email )

Milan
Italy

Franco Peracchi (Contact Author)

University of Rome Tor Vergata - Department of Economics and Finance ( email )

Via di Tor Vergata
Rome, Lazio 00133
Italy

Einaudi Institute for Economics and Finance (EIEF) ( email )

Via Due Macelli, 73
Rome, 00187
Italy

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
600
Abstract Views
2,249
Rank
82,851
PlumX Metrics