Semiparametrically efficient inference based on signs and ranks for median-restricted models
AbstractSince 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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Bibliographic InfoArticle 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 ()
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Other versions of this item:
- Hallin, M. & Vermandele, C. & Werker, B.J.M., 2004. "Semiparametrically Efficient Inference Based on Signs and Ranks for Median Restricted Models," Discussion Paper 2004-11, Tilburg University, Center for Economic Research.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
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- Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
- Hallin, M. & Puri, L.M., 1992.
"Aligned Rank tests for Linear Models with Autocorrelated Error Terms,"
9202, Universite Libre de Bruxelles - C.E.M.E..
- Hallin, M. & Puri, M. L., 1994. "Aligned Rank Tests for Linear Models with Autocorrelated Error Terms," Journal of Multivariate Analysis, Elsevier, vol. 50(2), pages 175-237, August.
- Marc Hallin & Bas Werker, 2003.
"Semiparametric efficiency, distribution-freeness, and invariance,"
ULB Institutional Repository
2013/2119, ULB -- Universite Libre de Bruxelles.
- Hallin, M. & Werker, B.J.M., 2003. "Semiparametric efficiency, distribution-freeness and invariance," Open Access publications from Tilburg University urn:nbn:nl:ui:12-117062, Tilburg University.
- Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January.
- Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1997. "Adaptive estimation in time-series models," Open Access publications from Tilburg University urn:nbn:nl:ui:12-74145, Tilburg University.
- repec:cup:etheor:v:11:y:1995:i:5:p:818-87 is not listed on IDEAS
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Hallin, M. & Vermandele, C. & Werker, B.J.M., 2006.
"Serial and nonserial sign-and-rank statistics. Asymptotic representation and asymptotic normality,"
Open Access publications from Tilburg University
urn:nbn:nl:ui:12-173772, Tilburg University.
- Hallin, M. & Vermandele, C. & Werker, B.J.M., 2003. "Serial and Nonserial Sign-and-Rank Statistics: Asymptotic Representation and Asymptotic Normality," Discussion Paper 2003-23, Tilburg University, Center for Economic Research.
- Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
- 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.
- 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.
- 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.
- Peter Hall, 2007. "Comments on: Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(3), pages 448-449, December.
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