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Medientyp:
E-Artikel
Titel:
Semiparametrically Efficient Inference Based on Signs and Ranks for Median-Restricted Models
Beteiligte:
Hallin, Marc;
Vermandele, Catherine;
Werker, Bas J. M.
Erschienen:
Oxford University Press (OUP), 2008
Erschienen in:
Journal of the Royal Statistical Society Series B: Statistical Methodology, 70 (2008) 2, Seite 389-412
Sprache:
Englisch
DOI:
10.1111/j.1467-9868.2007.00641.x
ISSN:
1467-9868;
1369-7412
Entstehung:
Anmerkungen:
Beschreibung:
SummarySince 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.