Large deviations of regression parameter estimate in the models with stationary sub-Gaussian noise
Author:
A. V. Ivanov
Journal:
Theor. Probability and Math. Statist. 95 (2017), 99-108
MSC (2010):
Primary 60G50, 65B10, 60G15; Secondary 40A05
DOI:
https://doi.org/10.1090/tpms/1024
Published electronically:
February 28, 2018
MathSciNet review:
3631646
Full-text PDF
Abstract |
References |
Similar Articles |
Additional Information
Abstract: Exponential bounds for probabilities of large deviations of nonlinear regression parameter least squares estimate in the models with jointly strictly sub-Gaussian random noise are obtained.
References
- A. V. Ivanov, Asymptotic expansions for distributions of least squares estimators of parameters of nonlinear regression, Teor. Verojatnost. i Primenen. 21 (1976), no. 3, 571–583 (Russian, with English summary). MR 0428547
- B. L. S. Prakasa Rao, On the exponential rate of convergence of the least squares estimator in the nonlinear regression model with Gaussian errors, Statist. Probab. Lett. 2 (1984), no. 3, 139–142. MR 747613, DOI https://doi.org/10.1016/0167-7152%2884%2990004-X
- Arthur Sieders and Kacha Dzhaparidze, A large deviation result for parameter estimators and its application to nonlinear regression analysis, Ann. Statist. 15 (1987), no. 3, 1031–1049. MR 902244, DOI https://doi.org/10.1214/aos/1176350491
- I. A. Ibragimov and R. Z. Has′minskiĭ, Statistical estimation, Applications of Mathematics, vol. 16, Springer-Verlag, New York-Berlin, 1981. Asymptotic theory; Translated from the Russian by Samuel Kotz. MR 620321
- Alexander V. Ivanov, Asymptotic theory of nonlinear regression, Mathematics and its Applications, vol. 389, Kluwer Academic Publishers Group, Dordrecht, 1997. MR 1472234
- A. V. Ivanov and N. N. Leonenko, Statistical analysis of random fields, Mathematics and its Applications (Soviet Series), vol. 28, Kluwer Academic Publishers Group, Dordrecht, 1989. With a preface by A. V. Skorokhod; Translated from the Russian by A. I. Kochubinskiĭ. MR 1009786
- B. L. S. Prakasa Rao, The rate of convergence of the least squares estimator in a nonlinear regression model with dependent errors, J. Multivariate Anal. 14 (1984), no. 3, 315–322. MR 747260, DOI https://doi.org/10.1016/0047-259X%2884%2990036-8
- Shu He Hu, A large deviation result for the least squares estimators in nonlinear regression, Stochastic Process. Appl. 47 (1993), no. 2, 345–352. MR 1239845, DOI https://doi.org/10.1016/0304-4149%2893%2990022-V
- Wenzhi Yang and Shuhe Hu, Large deviation for a least squares estimator in a nonlinear regression model, Statist. Probab. Lett. 91 (2014), 135–144. MR 3208127, DOI https://doi.org/10.1016/j.spl.2014.04.022
- Xufeng Huang, Xufei Tang, Xin Deng, and Xuejun Wang, The large deviation for the least squares estimator of nonlinear regression model based on WOD errors, J. Inequal. Appl. , posted on (2016), Paper No. 125, 11. MR 3489878, DOI https://doi.org/10.1186/s13660-016-1064-6
- J. Pfanzagl, On the measurability and consistency of minimum contrast estimates, J. Metrika 14 (1969), 249–272.
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, Translations of Mathematical Monographs, vol. 188, American Mathematical Society, Providence, RI, 2000. Translated from the 1998 Russian original by V. Zaiats. MR 1743716
- William Feller, An introduction to probability theory and its applications. Vol. I, John Wiley and Sons, Inc., New York; Chapman and Hall, Ltd., London, 1957. 2nd ed. MR 0088081
- I. I. Gikhman and A. V. Skorokhod, Introduction to the theory of random processes, Dover Publications, Inc., Mineola, NY, 1996. Translated from the 1965 Russian original; Reprint of the 1969 English translation; With a preface by Warren M. Hirsch. MR 1435501
- Peter J. Brockwell and Richard A. Davis, Introduction to time series and forecasting, 2nd ed., Springer Texts in Statistics, Springer-Verlag, New York, 2002. With 1 CD-ROM (Windows). MR 1894099
References
- A. V. Ivanov, An asymptotic expansion for the distribution of the least squares estimator of the non-linear regression parameter, Theory. Probab. Appl. 21 (1977), no. 3, 557–570. MR 0428547
- B. L. S. Prakasa Rao, On the exponential rate convergence of the least squares estimator in the nonlinear regression model with Gaussian errors, Statist. Probab. Lett. 2 (1984), 139–142. MR 747613
- A. Sieders and K. O. Dzhaparidze, A large deviation result for parameter estimators and its application to nonlinear regression analysis, Ann. Statist. 15 (1987), no. 3, 1031–1049. MR 902244
- I. A. Ibragimov and R. Z. Has’minskii, Statistical Estmation: Asymptotic Theory, Springer, New York, 1981. MR 620321
- A. V. Ivanov, Asymptotic Theory of Nonlinear Regression, Kluwer, Dordecht–Boston–London, 1997. MR 1472234
- A. V. Ivanov and N. N. Leonenko, Statistical Analysis of Random Fields, Kluwer, Dordecht–Boston–London, 1989. MR 1009786
- B. L. S. Prakasa Rao, The rate of convergence for the least squares estimator in a non-linear regression model with dependent errors, J. Multivariate Analysis 14 (1984), no. 3, 315–322. MR 747260
- S. H. Hu, A large deviation result for the least squares estimators in nonlinear regression, Stochastic Process and their Applications 47 (1993), 345–352. MR 1239845
- W. Z. Yang and S. H. Hu, Large deviation for a least squares estimator in a nonlinear regression model, Stat. Probab. Lett. 91 (2014), 135–144. MR 3208127
- X. Huang et al., The large deviation for the least squares estimator of nonlinear regression model based on WOD errors, J. Inequal. Appl. 125 (2016), (DOI: 10.1186/s13660-016-1064-6). MR 3489878
- J. Pfanzagl, On the measurability and consistency of minimum contrast estimates, J. Metrika 14 (1969), 249–272.
- V. V. Buldygin and Yu. V. Kozachenko, Metric characterization of random variables and random processes, AMS, Providence, RI, 2000. MR 1743716
- W. Feller, An Introduction to Probability Theory and its Applications, vol. 1, 2nd edition, Wiley, New York, 1957. MR 0088081
- I. I. Gikhman and A. V. Skorokhod, Introduction to the Theory of Random Processes, Dover Publications, Inc., 1996. MR 1435501
- P. J. Brockwell and R. A. Davis, Introduction to Time Series and Forecasting, 2nd Edition, Springer, New York, 2002. MR 1894099
Similar Articles
Retrieve articles in Theory of Probability and Mathematical Statistics
with MSC (2010):
60G50,
65B10,
60G15,
40A05
Retrieve articles in all journals
with MSC (2010):
60G50,
65B10,
60G15,
40A05
Additional Information
A. V. Ivanov
Affiliation:
Department of Mathematical Analysis and Probability Theory, Faculty of Physics and Mathematics, NTUU“KPI”, Kyiv, Ukraine
Email:
alexntuu@gmail.com
Keywords:
Large deviations,
least squares estimate,
nonlinear regression,
discrete white sub-Gaussian noise,
spectral density
Received by editor(s):
August 29, 2016
Published electronically:
February 28, 2018
Article copyright:
© Copyright 2018
American Mathematical Society
