The asymptotic normality of the Koenker–Bassett estimators in nonlinear regression models
Authors:
O. V. Ivanov and I. V. Orlovskiĭ
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 72 (2006), 33-45
MSC (2000):
Primary 62J02; Secondary 62J99
DOI:
https://doi.org/10.1090/S0094-9000-06-00662-4
Published electronically:
August 10, 2006
MathSciNet review:
2168134
Full-text PDF Free Access
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Additional Information
Abstract: The asymptotic normality of the Koenker–Bassett estimators of parameters of a nonlinear regression model with discrete time and independent errors of observations is studied in the paper.
References
- Roger Koenker and Gilbert Bassett Jr., Regression quantiles, Econometrica 46 (1978), no. 1, 33–50. MR 474644, DOI https://doi.org/10.2307/1913643
- Peter J. Huber, Robust statistics, John Wiley & Sons, Inc., New York, 1981. Wiley Series in Probability and Mathematical Statistics. MR 606374
- Alexander V. Ivanov, Asymptotic theory of nonlinear regression, Mathematics and its Applications, vol. 389, Kluwer Academic Publishers Group, Dordrecht, 1997. MR 1472234
- I. V. Orlovskiĭ, Consistency of Koenker–Bassett estimators in nonlinear regression models, Naukovi Visti NTUU “KPI” 3 (2004), 144–152. (Ukrainian)
- Tae Soo Kim and Hae Kyung Kim, Consistency of regression quantile estimators for the nonlinear time series regression model, Far East J. Theor. Stat. 5 (2001), no. 1, 181–191. MR 1848451
- Peter J. Huber, The behavior of maximum likelihood estimates under nonstandard conditions, Proc. Fifth Berkeley Sympos. Math. Statist. and Probability (Berkeley, Calif., 1965/66) Univ. California Press, Berkeley, Calif., 1967, pp. 221–233. MR 0216620
- R. N. Bhattacharya and R. Ranga Rao, Normal approximation and asymptotic expansions, John Wiley & Sons, New York-London-Sydney, 1976. Wiley Series in Probability and Mathematical Statistics. MR 0436272
References
- R. Koenker and G. Bassett, Regression quantile, Econometrica 46 (1978), 33–50. MR 0474644 (57:14279)
- P. J. Huber, Robust Statistics, Wiley, New York, 1981. MR 0606374 (82i:62057)
- A. V. Ivanov, Asymptotic Theory of Nonlinear Regression, Kluwer Academic Publishers, Dordrecht, 1997. MR 1472234 (99h:62086)
- I. V. Orlovskiĭ, Consistency of Koenker–Bassett estimators in nonlinear regression models, Naukovi Visti NTUU “KPI” 3 (2004), 144–152. (Ukrainian)
- Tae Soo Kim and Hae Kyung Kim, Consistency of regression quantile estimators for the nonlinear time series regression model, Far East J. Theor. Stat. 5(1) (2001), 181–191. MR 1848451 (2002g:62101)
- P. J. Huber, The behavior of maximum likelihood estimates under nonstandard conditions, Proc. Fifth Berkeley Sympos. Math. Statist. Probability. I, Univ. California Press, Berkeley, 1967, 221–234. MR 0216620 (35:7449)
- R. N. Bhattacharya and R. Ranga Rao, Normal Approximation and Asymptotic Expansions, Wiley, New York, 1976. MR 0436272 (55:9219)
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Additional Information
O. V. Ivanov
Affiliation:
National Technical University of Ukraine (KPI), Peremogy Avenue 37, Kyiv, Ukraine
Email:
ivanov@paligora.kiev.ua
I. V. Orlovskiĭ
Affiliation:
National Technical University of Ukraine (KPI), Peremogy Avenue 37, Kyiv, Ukraine
Received by editor(s):
March 19, 2004
Published electronically:
August 10, 2006
Article copyright:
© Copyright 2006
American Mathematical Society
