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Semiparametrically efficient inference based on signs and ranks for median-restricted models

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Author Info
Marc Hallin
Catherine Vermandele
Bas J. M. Werker

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Abstract

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. Copyright (c) 2008 The Authors.

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File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9868.2007.00641.x
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Publisher Info
Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 70 (2008)
Issue (Month): 2 ()
Pages: 389-412
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Handle: RePEc:bla:jorssb:v:70:y:2008:i:2:p:389-412

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References listed on IDEAS
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  1. Jeganathan, P., 1995. "Some Aspects of Asymptotic Theory with Applications to Time Series Models," Econometric Theory, Cambridge University Press, vol. 11(05), pages 818-887, October. [Downloadable!]
  2. Hallin, M. & Puri, L.M., 1992. "Aligned Rank tests for Linear Models with Autocorrelated Error Terms," Papers 9202, Universite Libre de Bruxelles - C.E.M.E..
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  3. repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
  4. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January. [Downloadable!] (restricted)
  5. Drost, F.C. & Klaasens, C.A.J. & Werker, B.J.M., 1994. "Adaptive Estimation in Time Series Models," Papers 9488, Tilburg - Center for Economic Research.
  6. Zhou, Yong & Liang, Hua, 2000. "Asymptotic Normality for L1 Norm Kernel Estimator of Conditional Median under [alpha]-Mixing Dependence," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 136-154, April. [Downloadable!] (restricted)
  7. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun. [Downloadable!] (restricted)
  8. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January. [Downloadable!] (restricted)
  9. Werker, B. & Vermandele, C. & Hallin, M., 2003. "Serial and nonserial sign-and-rank statistics: asymptotic representation and asymptotic normality," Discussion Paper 23, Tilburg University, Center for Economic Research. [Downloadable!]
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