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A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"

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  • Xu, Jianjun
  • Tan, Xianming
  • Zhang, Runchu
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    Abstract

    Phillips [Phillips R.F., 1991. A constrained maximum likelihood approach to estimating switching regressions. Journal of Econometrics 48, 241-262] proposed a constrained maximum-likelihood approach to estimating the parameters in a switching regression model. In this note, we propose a new approach which leads to a proof of a more general result than Phillips's. Specifically, we prove that the Constrained MLE (CMLE) is still strongly consistent when the constant c decreases to 0 at the rate of as n increases to [infinity], with [alpha]>1. We also suggest a suitable [alpha], hence cn, for practice based on simulation results.

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    File URL: http://www.sciencedirect.com/science/article/B6VC0-4WT3WM6-1/2/a2ea3c9bb6e68d18c776a0d2d0fb70dc
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 154 (2010)
    Issue (Month): 1 (January)
    Pages: 35-41

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    Handle: RePEc:eee:econom:v:154:y:2010:i:1:p:35-41

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Consistency Constrained maximum likelihood estimator Singularity Switching regression VC class;

    References

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    1. Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
    2. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-34, March.
    3. Devroye, Luc, 1982. "Bounds for the uniform deviation of empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 72-79, March.
    4. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    5. Smith, Aaron D. & Naik, Prasad A. & Tsai, Chih-Ling, 2005. "Markov-Switching Model Selection Using Kullback-Leibler Divergence," Working Papers 11976, University of California, Davis, Department of Agricultural and Resource Economics.
    6. Hartley, Michael J & Mallela, Parthasaradhi, 1977. "The Asymptotic Properties of a Maximum Likelihood Estimator for a Model of Markets in Disequilibrium," Econometrica, Econometric Society, vol. 45(5), pages 1205-20, July.
    7. Naik, Prasad A. & Shi, Peide & Tsai, Chih-Ling, 2007. "Extending the Akaike Information Criterion to Mixture Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 244-254, March.
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