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Finite-sample distribution of regression quantiles

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  • Jurecková, Jana

Abstract

The finite-sample distributions of the regression quantile and of the extreme regression quantile are derived for a broad class of distributions of the model errors, even for the non-i.i.d case. The distributions are analogous to the corresponding distributions in the location model; this again confirms that the regression quantile is a straightforward extension of the sample quantile. As an application, the tail behavior of the regression quantile is studied.

Suggested Citation

  • Jurecková, Jana, 2010. "Finite-sample distribution of regression quantiles," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1940-1946, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1940-1946
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    References listed on IDEAS

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, November.
    3. Marc Hallin & Jana Jureckova, 1999. "Optimal tests for autoregressive models based on autoregression rank scores," ULB Institutional Repository 2013/2089, ULB -- Universite Libre de Bruxelles.
    4. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    5. Jana Jurečková & Jan Picek & Pranab Sen, 2003. "Goodness-of-fit test with nuisance regression and scale," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 58(3), pages 235-258, December.
    6. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
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    1. Jurečková, Jana & Picek, Jan, 2012. "Regression quantiles and their two-step modifications," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1111-1115.
    2. Jurecková, Jana & Sabolová, Radka, 2011. "Finite-sample density and its small sample asymptotic approximation," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1311-1318, August.
    3. Neykov, N.M. & Čížek, P. & Filzmoser, P. & Neytchev, P.N., 2012. "The least trimmed quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1757-1770.

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