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
Date Written: 2004
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: Suggested Citation