Regression quantiles and trimmed least squares estimator under a general design. (English) Zbl 0561.62027

For the linear model with i.i.d. error terms, the author obtains the Bahadur-type representation of regression quantiles, the asymptotic representation and the asymptotic distribution of the trimmed least squares estimator.
Reviewer: S.Wang


62F35 Robustness and adaptive procedures (parametric inference)
62J05 Linear regression; mixed models
62E20 Asymptotic distribution theory in statistics
Full Text: EuDML


[1] R. R. Bahadur: A note on quantiles in large samples. Ann. Math. Statist. 37 (1966), 577-580. · Zbl 0147.18805
[2] G. Bassett, R. Koenker: An empirical quantile function for linear models with iid errors. J. Amer. Statist. Assoc. 77 (1982), 407-415. · Zbl 0493.62047
[3] G. Bassett, R. Koenker: Convergence of an empirical distribution function for the linear model. Submitted (1983).
[4] P. J. Bickel: On some analogues to linear combinations of order statistics in the linear model. Ann. Statist. / (1973), 597-616. · Zbl 0265.62021
[5] P. Billingsley: Convergence of Probability Measures. J. Wiley, New York, 1968. · Zbl 0172.21201
[6] P. J. Huber: Robust Statistics. J. Wiley, New York 1981. · Zbl 0536.62025
[7] L. A. Jaeckel: Estimating regression coefficients by minimizing the dispersion of the residuals. Ann. Math. Statist. 43 (1972), 1449-1458. · Zbl 0277.62049
[8] J. Jurečková: Nonparametric estimate of regression coefficients. Ann. Math. Statist. 42 (1971), 1328-1338. · Zbl 0225.62052
[9] J. Jurečková: Asymptotic independence of rank test statistic for testing symmetry on regression. Sankhya A 33 (1971), 1-18. · Zbl 0226.62040
[10] J. Jurečková: Asymptotic relations of M-estimates and R-estimates in linear regression model. Ann. Statist. 5 (1977), 464-472.
[11] J. Jurečková: Asymptotic representation of M-estimators of location. Math. Operations-forsch. Statist., Ser. Statistics 11 (1980), 61-73.
[12] J. Jurečková: Robust estimators of location and regression parameters and their second order asymptotic relations. Trans. 9th Prague Conf. on Inform. Theory, Statist. Dec. Functions and Random Processes, pp. 19-32. Academia, Praha 1983.
[13] J. Jurečková: Winsorized least-squares estimator and its M-estimator counterpart. Contributions to Statistics: Essays in Honour of Norman L. Johnson (ed. P. K. Sen), pp. 237- 245. North-Holland, Amsterdam 1983. · Zbl 0533.62035
[14] J. Jurečková, P. K. Sen: On adaptive scale-equivariant M-estimators in linear models. Statistics and Decisions 2, (1984), to appear. · Zbl 0586.62042
[15] R. Koenker: A note on L-estmates for linear models. Preprint. Bell Laboratories, Murray- Hill (1983).
[16] R. Koenker, G. Bassett: Regression quantiles. Econometrica 46 (1978), 33 - 50. · Zbl 0373.62038
[17] H. L. Koul: Asymptotic behavior of a class of confidence regions based on ranks in regression. Ann. Math. Statist. 42 (1971), 466-476. · Zbl 0215.54204
[18] S. Portnoy: Tightness of the sequence of empiric c.d.f. processes defined from regression fractiles. Submitted (1983). · Zbl 0568.62065
[19] D. Ruppert, R. J. Carroll: Trimmed least-squares estimation in the linear model. J. Amer. Statist. Assoc. 75 (1980), 828-838. · Zbl 0459.62055
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