Semiparametrically efficient inference based on signs and ranks for median-restricted models
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 tha...
Saved in:
Published in | Journal of the Royal Statistical Society. Series B, Statistical methodology Vol. 70; no. 2; pp. 389 - 412 |
---|---|
Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Oxford, UK
Oxford, UK : Blackwell Publishing Ltd
01.01.2008
Blackwell Publishing Ltd Blackwell Publishing Blackwell Royal Statistical Society Oxford University Press |
Series | Journal of the Royal Statistical Society Series B |
Subjects | |
Online Access | Get full text |
Cover
Loading…
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. |
---|---|
Bibliography: | http://dx.doi.org/10.1111/j.1467-9868.2007.00641.x ArticleID:RSSB641 istex:AEA108B614C5D4C3633F4E6CDCEA9D1945AE53E8 ark:/67375/WNG-FWV9J0HS-S ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
ISSN: | 1369-7412 1467-9868 |
DOI: | 10.1111/j.1467-9868.2007.00641.x |