Semi-Parametrically Efficient Inference-Based on Signs and Ranks for Median-Restricted Models

CentER Discussion Paper No. 2004-11

40 Pages Posted: 21 Jun 2004

See all articles by Marc Hallin

Marc Hallin

ECARES, Universite Libre de Bruxelles

Catherine Vermandele

Université Libre de Bruxelles (ULB)

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: 2004

Abstract

Since the pioneering work of Koenker and Bassett (1978), econometric models involving median and quantile, rather than the classical mean or conditional mean concepts, have attracted much interest. Contrary to the traditional models where the noise is assumed to have mean zero, median-restricted models enjoy a rich group-invariance structure. In this paper, we exploit this invariance structure in order to obtain semi-parametrically efficient inference procedures for these models. These procedures are based on residual signs and ranks, and, therefore, insensitive to possible misspecification of the underlying innovation density, yet semi-parametrically efficient at correctly specified densities. This latter combination is a definite advantage of these procedures over classical quasi-likelihood methods. The techniques we propose can be applied, without additional technical difficulties, to both cross-sectional and time-series models. They do not require any explicit tangent space calculation nor any projections on these.

Keywords: Invariance structure, local asymptotic normality, median regression, quantile restrictions

JEL Classification: C14

Suggested Citation

Hallin, Marc and Vermandele, Catherine and Werker, Bas J.M., Semi-Parametrically Efficient Inference-Based on Signs and Ranks for Median-Restricted Models (2004). CentER Discussion Paper No. 2004-11, Available at SSRN: https://ssrn.com/abstract=556973 or http://dx.doi.org/10.2139/ssrn.556973

Marc Hallin (Contact Author)

ECARES, Universite Libre de Bruxelles ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium
+32 2 650 5886 (Phone)
+32 2 650 5899 (Fax)

Catherine Vermandele

Université Libre de Bruxelles (ULB) ( email )

CP 132 Av FD Roosevelt 50
Brussels, Brussels 1050
Belgium

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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