Semiparametrically efficient inference based on signs and ranks for median‐restricted models
Marc Hallin (),
Catherine Vermandele and
Bas J. M. Werker
Journal of the Royal Statistical Society Series B, 2008, vol. 70, issue 2, 389-412
Summary. Since the pioneering work of Koenker and Bassett, median‐restricted models have attracted considerable interest. Attention in these models, so far, has focused on least absolute deviation (auto‐)regression quantile estimation and the corresponding sign tests. These methods use a pseudolikelihood that is based on a double‐exponential reference density and enjoy quite attractive properties of root n consistency (for estimators) and distribution freeness (for tests). The paper extends these results to general, i.e. not necessarily double‐exponential, reference densities. Using residual signs and ranks (not signed ranks) and a general reference density f, we construct estimators that remain root n consistent, irrespective of the true underlying density g (i.e. also for g /=f). However, instead of reaching semiparametric efficiency bounds under double‐exponential g, they reach these bounds when g coincides with the chosen reference density f. Moreover, we show that choosing reference densities other than the double‐exponential in applications can lead to sizable gains in efficiency. The particular case of median regression is treated in detail; extensions to general quantile regression, heteroscedastic errors and time series models are briefly described. The performance of the method is also assessed by simulation and illustrated on financial data.
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Working Paper: Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models (2004)
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