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Strong convergence of estimators in nonlinear autoregressive models

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  • Liebscher, Eckhard
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    Abstract

    In the paper we prove rates of strong convergence of M-estimators for the parameters in a general nonlinear autoregressive model. In the proofs we utilize a variational principle from stochastic optimization theory which was proved by Shapiro (Ann. Oper. Res. 30 (1991) 169). The application of the general theory is illustrated in the case of continuous threshold models.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 84 (2003)
    Issue (Month): 2 (February)
    Pages: 247-261

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    Handle: RePEc:eee:jmvana:v:84:y:2003:i:2:p:247-261

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    Related research

    Keywords: Nonlinear autoregressive model M-estimators Strong convergence Threshold models;

    References

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    1. Liebscher, Eckhard, 1996. "Strong convergence of sums of [alpha]-mixing random variables with applications to density estimation," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 69-80, December.
    2. Huang, Sun Young & Basawa, I. V., 1994. "Large sample inference based on multiple observations from nonlinear autoregressive processes," Stochastic Processes and their Applications, Elsevier, vol. 49(1), pages 127-140, January.
    3. Liebscher E., 2001. "Estimation Of The Density And The Regression Function Under Mixing Conditions," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 9-26, January.
    4. Arcones, Miguel A., 1994. "Some strong limit theorems for M-estimators," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 241-268, October.
    5. Potscher, Benedikt M. & Prucha, Ingmar R., 1986. "A class of partially adaptive one-step m-estimators for the non-linear regression model with dependent observations," Journal of Econometrics, Elsevier, vol. 32(2), pages 219-251, July.
    6. Tjøstheim, Dag, 1986. "Estimation in nonlinear time series models," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 251-273, February.
    7. Liese, F. & Vajda, I., 1994. "Consistency of M-Estimates in General Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 50(1), pages 93-114, July.
    8. Koul, Hira L. & Zhu, Zhiwei, 1995. "Bahadur-Kiefer representations for GM-estimators in autoregression models," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 167-189, May.
    9. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(02), pages 258-289, February.
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    Cited by:
    1. Jonathan Hill, 2006. "Asymptotically Nuisance-Parameter-Free Consistent Tests of Lp-Functional Form," Working Papers 0608, Florida International University, Department of Economics.

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