Premium
Semiparametrically efficient inference based on signs and ranks for median‐restricted models
Author(s) -
Hallin Marc,
Vermandele Catherine,
Werker Bas J. M.
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2007.00641.x
Subject(s) - estimator , quantile , mathematics , consistency (knowledge bases) , heteroscedasticity , statistics , exponential function , double exponential function , quantile regression , sign (mathematics) , inference , residual , series (stratigraphy) , econometrics , regression , asymptotic distribution , least absolute deviations , algorithm , computer science , mathematical analysis , discrete mathematics , artificial intelligence , paleontology , biology
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.