Consistency of quantile estimators in regression models with long-range dependent noise
Author:
I. M. Savich
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 82 (2011), 129-138
MSC (2010):
Primary 62J02; Secondary 62J99
DOI:
https://doi.org/10.1090/S0094-9000-2011-00832-0
Published electronically:
August 4, 2011
MathSciNet review:
2790488
Full-text PDF Free Access
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Additional Information
Abstract: Sufficient conditions for weak consistency of the Koenker–Bassett estimator are obtained for the parameter of a nonlinear regression model with continuous time and random noise possessing the property of the long-range dependence.
References
- Jan Beran, Statistics for long-memory processes, Monographs on Statistics and Applied Probability, vol. 61, Chapman and Hall, New York, 1994. MR 1304490
- Nikolai Leonenko, Limit theorems for random fields with singular spectrum, Mathematics and its Applications, vol. 465, Kluwer Academic Publishers, Dordrecht, 1999. MR 1687092
- Paul Doukhan, George Oppenheim, and Murad S. Taqqu (eds.), Theory and applications of long-range dependence, Birkhäuser Boston, Inc., Boston, MA, 2003. MR 1956041
- Roger Koenker and Gilbert Bassett Jr., Regression quantiles, Econometrica 46 (1978), no. 1, 33–50. MR 474644, DOI https://doi.org/10.2307/1913643
- I. V. Orlovs’kiĭ, Consistence of Koenker–Bassett estimators in nonlinear regression models, Naukovi visti NTUU “KPI” 35 (2004), no. 3, 144–150. (Ukrainian)
- O. V. Īvanov and Ī. V. Orlovs′kiĭ, Asymptotic normality of Koenker-Bassett estimators in nonlinear regression models, Teor. Ĭmovīr. Mat. Stat. 72 (2005), 30–41 (Ukrainian, with Ukrainian summary); English transl., Theory Probab. Math. Statist. 72 (2006), 33–45. MR 2168134, DOI https://doi.org/10.1090/S0094-9000-06-00662-4
- Eugene Seneta, Regularly varying functions, Lecture Notes in Mathematics, Vol. 508, Springer-Verlag, Berlin-New York, 1976. MR 0453936
- J. Pfanzagl, On the measurability and consistency of minimum contrast estimates, Metrika 14 (1969), 249–272.
- A. V. Ivanov and I. V. Orlovsky, $L_{p}$ estimates in nonlinear regression with long-range dependence, Theory Stoch. Process. 7(23) (2002), no. 3–4, 38–49.
References
- J. Beran, Statistics for Long-Memory Processes, Chapman and Hall, New York, 1994. MR 1304490 (96b:62138)
- N. N. Leonenko, Limit Theorems for Random Fields with Singular Spectrum, Kluwer Academic Publishers, Dordrecht, 1999. MR 1687092 (2000k:60102)
- P. Doukhan, G. Oppenheim, and M. S. Taqqu, Theory and Applications of Long-Range Dependence, Birkhäuser, Boston, 2003. MR 1956041 (2003h:60004)
- G. Bassett and R. Koenker, Regression quantile, Econometrica (G. Bassett and R. Koenker, eds.), vol. 46, 1978, pp. 33–50. MR 0474644 (57:14279)
- I. V. Orlovs’kiĭ, Consistence of Koenker–Bassett estimators in nonlinear regression models, Naukovi visti NTUU “KPI” 35 (2004), no. 3, 144–150. (Ukrainian)
- O. V. Ivanov and I. V. Orlovs’kiĭ, Asymptotic normality of Koenker–Bassett estimators in nonlinear regression models, Teor. Imovir. Mat. Stat. 72 (2005), 30–41; English transl. in Theory Probab. Math. Statist. 72 (2006), 33–45. MR 2168134 (2007b:62029)
- E. Seneta, Regularly Varying Functions, Springer-Verlag, Berlin–New York, 1976. MR 0453936 (56:12189)
- J. Pfanzagl, On the measurability and consistency of minimum contrast estimates, Metrika 14 (1969), 249–272.
- A. V. Ivanov and I. V. Orlovsky, $L_{p}$ estimates in nonlinear regression with long-range dependence, Theory Stoch. Process. 7(23) (2002), no. 3–4, 38–49.
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Additional Information
I. M. Savich
Affiliation:
Department of Mathematical Analysis and Probability Theory, National Technical University of Ukraine “Kyiv Polytechnic Institute”, Peremogy Avenue 37, Kyiv–56 03056, Ukraine
Email:
sim_ka@i.ua
Keywords:
Quantile estimators,
consistency,
nonlinear regression models,
noise with long-range memory
Received by editor(s):
December 1, 2009
Published electronically:
August 4, 2011
Article copyright:
© Copyright 2011
American Mathematical Society
