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Nonparametric Estimation using Regression Quantiles in a Regression Model

  • Received : 2012.08.11
  • Accepted : 2012.09.21
  • Published : 2012.10.31

Abstract

One proposal is made to construct a nonparametric estimator of slope parameters in a regression model under symmetric error distributions. This estimator is based on the use of the idea of minimizing approximate variance of a proposed estimator using regression quantiles. This nonparametric estimator and some other L-estimators are studied and compared with well known M-estimators through a simulation study.

Keywords

Regression quantile;regression trimmed mean;L-estimator

References

  1. Adichie, J. N. (1974). Rank score comparison of several regression parameter, Annals of Statistics, 2, 396- 402. https://doi.org/10.1214/aos/1176342676
  2. Barrodale, I. and Roberts, F. D. K. (1974). Solution of an overdetermined system of equations in the L norm, Communications of the Association for Computing Machinery, 17, 407-415.
  3. Bickel, P. J. (1973). On some analogues to linear combinations of ordered statistics in the linear model, Annals of Statistics, 1, 597-616. https://doi.org/10.1214/aos/1176342457
  4. DasGupta, P. J. (2008). Asymptotic Theory of Statistics and Probability, Springer.
  5. De Jongh, P. J. and De Wet, T. (1985). A Monte Carlo comparison of regression trimmed means, Communications in Statistics - Theory and Methods, 10, 2457-2472.
  6. Hampel, F. R., Ronchetti, E. M., Rousseeuw, P. M. and Stahel, W. A. (1986). Robust Statistics, the Approach Based on Influence Function, John Wiley.
  7. Han, S. M. (2003). Adaptive M-estimation in regression model, The Korean Communications in Statistics, 10, 859-871. https://doi.org/10.5351/CKSS.2003.10.3.859
  8. Hettmansperger, T. P. and McKean, J. W. (1977). A robust alternative based on ranks to least squares in analyzing linear models, Technometircs, 19, 275-284. https://doi.org/10.1080/00401706.1977.10489549
  9. Hogg, R. V. (1983). On adaptive statistical inference, Communications in Statistics - Theory and Methods, 11, 2531-2542.
  10. Hogg, R. V., Bril, G. K., Han, S. M. and Yuh, L. (1988). An argument for adaptive Robust estimation, Probability and Statistics, Essays in Honor of Graybill, F. A., North Holland, 135-148.
  11. Holland, P. W. and Welsch, R. E. (1977). Robust regression using iteratively reweighted least-squares, Communications in Statistics - Theory and Methods, 6, 813-827. https://doi.org/10.1080/03610927708827533
  12. Huber, P. J. (1973). Robust regression: Asymptotics, Conjectures and Monte Carlo, Annals of statistics, 1, 799-821. https://doi.org/10.1214/aos/1176342503
  13. Huber, P. J. (1981). Robust Statistics, John Wiley.
  14. Jaeckel, L. A. (1971). Robust estimates of location: Symmetry and asymmetric contamination, The Annals of Mathematical Statistics, 42, 1020-1034. https://doi.org/10.1214/aoms/1177693330
  15. Johns, M. V. (1974). Nonparametric estimation of location, Journal of the American Statistical Association, 69, 453-460. https://doi.org/10.1080/01621459.1974.10482973
  16. Koenker, R. and Bassett, C. (1978). Regression quantiles, Econometrica, 46, 33-50. https://doi.org/10.2307/1913643
  17. Koenker, R. and Bassett, C. (1982). Robust tests for Heterosedasticity based on regression quantiles, Econometrica, 50, 43-61. https://doi.org/10.2307/1912528
  18. Koenker, R., Hammond, P. and Holly, A. (2005). Quantile Regression, Cambridge University Press.
  19. Portnoy, S. and Koenker, R. (1997). The Gaussian Hare and the Laplacian Tortoise: Computability of squared-error versus absolute-error estimators, Statistical Science, 12, 299-300.
  20. Ruppert, D. and Carroll, R. J. (1980). Trimmed least squares estimation in the linear model, Journal of the American Statical Association, 75, 828-838. https://doi.org/10.1080/01621459.1980.10477560

Acknowledgement

Supported by : University of Seoul