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Linearization Of Randomly Weighted Empiricals Under Long Range Dependence With Applications To Nonlinear Regression Quantiles

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  • Mukherjee, Kanchan

Abstract

This paper discusses some asymptotic uniform linearity results of randomly weighted empirical processes based on long range dependent random variables. These results are subsequently used to linearize nonlinear regression quantiles in a nonlinear regression model with long range dependent errors, where the design variables can be either random or nonrandom. These, in turn, yield the limiting behavior of the nonlinear regression quantiles. As a corollary, we obtain the limiting behavior of the least absolute deviation estimator and the trimmed mean estimator of the parameters of the nonlinear regression model. Some of the limiting properties are in striking contrast with the corresponding properties of a nonlinear regression model under independent and identically distributed error random variables. The paper also discusses an extension of rank score statistic in a nonlinear regression model.

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  • Mukherjee, Kanchan, 2000. "Linearization Of Randomly Weighted Empiricals Under Long Range Dependence With Applications To Nonlinear Regression Quantiles," Econometric Theory, Cambridge University Press, vol. 16(3), pages 301-323, June.
    • Handle: RePEc:cup:etheor:v:16:y:2000:i:03:p:301-323_16
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    References listed on IDEAS

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    1. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, vol. 50(3), pages 689-711, May.
    2. Portnoy, Stephen, 1991. "Asymptotic behavior of regression quantiles in non-stationary, dependent cases," Journal of Multivariate Analysis, Elsevier, vol. 38(1), pages 100-113, July.
    3. Weiss, Andrew A., 1991. "Estimating Nonlinear Dynamic Models Using Least Absolute Error Estimation," Econometric Theory, Cambridge University Press, vol. 7(1), pages 46-68, March.
    4. Mukherjee, Kanchan, 1994. "Minimum distance estimation in linear models with long-range dependent errors," Statistics & Probability Letters, Elsevier, vol. 21(5), pages 347-355, December.
    5. Koul, H. L. & Mukherjee, K., 1994. "Regression Quantiles and Related Processes Under Long Range Dependent Errors," Journal of Multivariate Analysis, Elsevier, vol. 51(2), pages 318-337, November.
    6. Koenker, Roger & Park, Beum J., 1996. "An interior point algorithm for nonlinear quantile regression," Journal of Econometrics, Elsevier, vol. 71(1-2), pages 265-283.
    7. 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. 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.
    2. 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.
    3. Mohsin, Muhammad & Taghizadeh-Hesary, Farhad & Shahbaz, Muhammad, 2022. "Nexus between financial development and energy poverty in Latin America," Energy Policy, Elsevier, vol. 165(C).

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