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On weak convergence of the likelihood ratio process in multi-phase regression models

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  • Fujii, Takayuki

Abstract

The purpose of this paper is to study the change point estimation problem in multi-phase regression models. This is a non-regular statistical estimation; thus the asymptotic distribution of the maximum likelihood estimator is verified by means of the weak convergence of the likelihood ratio process. These weak convergence results differ depending on the jump size of the regression function.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:14:p:2066-2074
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    References listed on IDEAS

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    1. Gut, Allan & Janson, Svante, 2001. "Tightness and weak convergence for jump processes," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 101-107, March.
    2. 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.
    3. Fujii, Takayuki, 2007. "A note on the asymptotic distribution of the maximum likelihood estimator in a non-regular case," Statistics & Probability Letters, Elsevier, vol. 77(16), pages 1622-1627, October.
    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. Sergueï Dachian & Lin Yang, 2015. "On a Poissonian change-point model with variable jump size," Statistical Inference for Stochastic Processes, Springer, vol. 18(2), pages 127-150, July.

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