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 semiparametrically 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 semiparametrically 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.
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Paper provided by Tilburg University, Center for Economic Research in its series Discussion Paper with number
11.
Find related papers by JEL classification: C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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