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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

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.

Suggested Citation

  • Xu, Jianjun & Tan, Xianming & Zhang, Runchu, 2010. "A note on Phillips (1991): "A constrained maximum likelihood approach to estimating switching regressions"," Journal of Econometrics, Elsevier, vol. 154(1), pages 35-41, January.
    • Handle: RePEc:eee:econom:v:154:y:2010:i:1:p:35-41
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    References listed on IDEAS

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    1. 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.
    2. Kiefer, Nicholas M, 1978. "Discrete Parameter Variation: Efficient Estimation of a Switching Regression Model," Econometrica, Econometric Society, vol. 46(2), pages 427-434, March.
    3. Amemiya, Takeshi, 1973. "Regression Analysis when the Dependent Variable is Truncated Normal," Econometrica, Econometric Society, vol. 41(6), pages 997-1016, November.
    4. Devroye, Luc, 1982. "Bounds for the uniform deviation of empirical measures," Journal of Multivariate Analysis, Elsevier, vol. 12(1), pages 72-79, March.
    5. Phillips, Robert F., 1991. "A constrained maximum-likelihood approach to estimating switching regressions," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 241-262.
    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 1205-1220, July.
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    Cited by:

    1. Roberto Rocci & Stefano Antonio Gattone & Roberto Di Mari, 2018. "A data driven equivariant approach to constrained Gaussian mixture modeling," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 12(2), pages 235-260, June.
    2. Libin Jin & Sung Nok Chiu & Jianhua Zhao & Lixing Zhu, 2023. "A constrained maximum likelihood estimation for skew normal mixtures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(4), pages 391-419, May.

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