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

  • Koul, Hira L.
  • Qian, Lianfen
  • Surgailis, Donatas
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    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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    File URL: http://www.sciencedirect.com/science/article/B6V1B-479KHK9-5/2/a092055af676125bffae3565b16b8e17
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    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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    1. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. 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.
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