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Large deviation for a least squares estimator in a nonlinear regression model

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  • Yang, Wenzhi
  • Hu, Shuhe

Abstract

By using a large deviation theory of the stochastic process and the moment information of errors, some large deviation results for the least squares estimator θn in a nonlinear regression model are obtained when errors satisfy some general conditions. For some p>1, examples are presented to show that our results can be used in the case for supn≥1E|ξn|p=∞ and a better bound can be obtained in the case for supn≥1E|ξn|p<∞. Our results generalize and improve the corresponding ones.

Suggested Citation

  • Yang, Wenzhi & Hu, Shuhe, 2014. "Large deviation for a least squares estimator in a nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 135-144.
    • Handle: RePEc:eee:stapro:v:91:y:2014:i:c:p:135-144
    DOI: 10.1016/j.spl.2014.04.022
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    References listed on IDEAS

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    1. Shuhe, Hu, 2004. "Consistency for the least squares estimator in nonlinear regression model," Statistics & Probability Letters, Elsevier, vol. 67(2), pages 183-192, April.
    2. Malyutov, Mikhail B. & Protassov, Rostislav S., 1999. "Functional approach to the asymptotic normality of the non-linear least squares estimator," Statistics & Probability Letters, Elsevier, vol. 44(4), pages 409-416, October.
    3. Prakasa Rao, B. L. S., 1984. "On the exponential rate of convergence of the least squares estimator in the nonlinear regression model with Gaussian errors," Statistics & Probability Letters, Elsevier, vol. 2(3), pages 139-142, May.
    4. Prakasa Rao, B. L. S., 1984. "The rate of convergence of the least squares estimator in a non-linear regression model with dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 14(3), pages 315-322, June.
    5. Prakasa Rao, B. L. S., 2004. "Estimation of cusp in nonregular nonlinear regression models," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 243-251, February.
    6. Hansen, Bruce E., 1991. "Strong Laws for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 7(2), pages 213-221, June.
    7. Habshah Midi, 1999. "Preliminary estimators for robust non-linear regression estimation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 26(5), pages 591-600.
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    Cited by:

    1. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
    2. Miao, Yu & Tang, Yanyan, 2021. "Large deviation inequalities of LS estimator in nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 168(C).
    3. Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    4. Yu Miao & Yanyan Tang, 2023. "Large deviation inequalities of Bayesian estimator in nonlinear regression models," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 171-191, April.

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