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The asymptotic distribution of the unconditional quantile estimator under dependence

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  • Oberhofer, Walter
  • Haupt, Harry

Abstract

This paper studies the asymptotic behaviour of the unconditional quantile estimator for dependent random variables. Our proof is based on results from convex stochastic optimization and a mixing process which is specific to quantile estimation and requires only a small part of the [sigma]-algebra generated by the random variable under consideration. The joint asymptotic distribution of several quantiles is given.

Suggested Citation

  • Oberhofer, Walter & Haupt, Harry, 2005. "The asymptotic distribution of the unconditional quantile estimator under dependence," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 243-250, July.
    • Handle: RePEc:eee:stapro:v:73:y:2005:i:3:p:243-250
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    References listed on IDEAS

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    1. Castellana, J. V. & Leadbetter, M. R., 1986. "On smoothed probability density estimation for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 179-193, February.
    2. De Gooijer J.G. & Zerom D., 2003. "On Additive Conditional Quantiles With High Dimensional Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 135-146, January.
    3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    4. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
    5. Cai, Zongwu, 2002. "Regression Quantiles For Time Series," Econometric Theory, Cambridge University Press, vol. 18(1), pages 169-192, February.
    6. Pollard, David, 1991. "Asymptotics for Least Absolute Deviation Regression Estimators," Econometric Theory, Cambridge University Press, vol. 7(2), pages 186-199, June.
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    Cited by:

    1. Dominicy, Yves & Hörmann, Siegfried & Ogata, Hiroaki & Veredas, David, 2013. "On sample marginal quantiles for stationary processes," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 28-36.
    2. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2011. "Likelihood-based scoring rules for comparing density forecasts in tails," Journal of Econometrics, Elsevier, vol. 163(2), pages 215-230, August.
    3. Oberhofer, Walter & Haupt, Harry, 2005. "Consistency of nonlinear regression quantiles under Type I censoring weak dependence and general covariate design," University of Regensburg Working Papers in Business, Economics and Management Information Systems 406, University of Regensburg, Department of Economics.
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    5. Oberhofer, Walter & Haupt, Harry, 2003. "Nonlinear quantile regression under dependence and heterogeneity," University of Regensburg Working Papers in Business, Economics and Management Information Systems 388, University of Regensburg, Department of Economics.
    6. Lajos Horváth & Gregory Rice, 2014. "Extensions of some classical methods in change point analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 219-255, June.

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