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Asymptotics of M-estimators in two-phase linear regression models

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  • Koul, Hira L.
  • Qian, Lianfen
  • Surgailis, Donatas
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    Abstract

    This paper discusses the consistency and limiting distributions of a class of M-estimators in two-phase random design linear regression models where the regression function is discontinuous at the change-point with a fixed jump size. The consistency rate of an M-estimator for the change-point parameter r is shown to be n while it is n1/2 for the coefficient parameter estimators, where n denotes the sample size. The normalized M-process is shown to be uniformly locally asymptotically equivalent to the sum of a quadratic form in the coefficient parameter vector and a jump point process in the change-point parameter, in probability. These results are then used to obtain the joint weak convergence of the M-estimators. In particular, is shown to converge weakly to a random variable which minimizes a compound Poisson process, a suitably standardized coefficient parameter M-estimator vector is shown to be asymptotically normal, and independent of .

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 103 (2003)
    Issue (Month): 1 (January)
    Pages: 123-154

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    Handle: RePEc:eee:spapps:v:103:y:2003:i:1:p:123-154

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    Related research

    Keywords: Change-point estimator Fixed jump size Compound Poisson process;

    References

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    1. Müller, Hans-Georg & Song, Kai-Sheng, 1997. "Two-stage change-point estimators in smooth regression models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 323-335, June.
    2. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
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    Cited by:
    1. Gill, Ryan & Lee, Kiseop & Song, Seongjoo, 2007. "Computation of estimates in segmented regression and a liquidity effect model," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6459-6475, August.
    2. Ciuperca, Gabriela, 2009. "The M-estimation in a multi-phase random nonlinear model," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 573-580, March.
    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.
    4. Dupuy, Jean-François, 2006. "Estimation in a change-point hazard regression model," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 182-190, January.
    5. Zhang, Li-Xin & Chan, Wai-Sum & Cheung, Siu-Hung & Hung, King-Chi, 2009. "A note on the consistency of a robust estimator for threshold autoregressive processes," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 807-813, March.
    6. Fujii, Takayuki, 2008. "On weak convergence of the likelihood ratio process in multi-phase regression models," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2066-2074, October.
    7. Gabriela Ciuperca, 2011. "Penalized least absolute deviations estimation for nonlinear model with change-points," Statistical Papers, Springer, vol. 52(2), pages 371-390, May.

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