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The M-estimation in a multi-phase random nonlinear model

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  • Ciuperca, Gabriela

Abstract

This paper extends the results of M-estimation in [Koul, H.L., Qian, L., Surgailis, D., 2003. Asymptotics of M-estimators in two-phase linear regression models. Stochastic Processes and their Applications, 103, 123-154] to a general nonlinear random design regression model with multiple change-points at unknown times. The M-estimator of locations of breaks and of regression parameters are consistent. Convergence rate and asymptotic distribution are obtained.

Suggested Citation

  • Ciuperca, Gabriela, 2009. "The M-estimation in a multi-phase random nonlinear model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 573-580, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:573-580
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    References listed on IDEAS

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    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Ciuperca Gabriela, 2004. "Maximum likelihood estimator in a two-phase nonlinear random regression model," Statistics & Risk Modeling, De Gruyter, vol. 22(4), pages 335-349, April.
    4. Koul, Hira L. & Qian, Lianfen & Surgailis, Donatas, 2003. "Asymptotics of M-estimators in two-phase linear regression models," Stochastic Processes and their Applications, Elsevier, vol. 103(1), pages 123-154, January.
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    Cited by:

    1. Müller, Ursula U. & Schick, Anton & Wefelmeyer, Wolfgang, 2015. "Estimators in step regression models," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 124-129.
    2. Gabriela Ciuperca, 2014. "Model selection by LASSO methods in a change-point model," Statistical Papers, Springer, vol. 55(2), pages 349-374, May.
    3. Ciuperca, Gabriela, 2011. "A general criterion to determine the number of change-points," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1267-1275, August.

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