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Using the Penalized Likelihood Method for Model Selection with Nuisance Parameters Present only under the Alternative: An Application to Switching Regression Models

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  • Arie Preminger
  • David Wettstein

Abstract

. We study the problem of model selection with nuisance parameters present only under the alternative. The common approach for testing in this case is to determine the true model through the use of some functionals over the nuisance parameters space. Since in such cases the distribution of these statistics is not known, critical values had to be approximated usually through computationally intensive simulations. Furthermore, the computed critical values are data and model dependent and hence cannot be tabulated. We address this problem by using the penalized likelihood method to choose the correct model. We start by viewing the likelihood ratio as a function of the unidentified parameters. By using the empirical process theory and the uniform law of the iterated logarithm (LIL) together with sufficient conditions on the penalty term, we derive the consistency properties of this method. Our approach generates a simple and consistent procedure for model selection. This methodology is presented in the context of switching regression models. We also provide some Monte Carlo simulations to analyze the finite sample performance of our procedure.

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  • Arie Preminger & David Wettstein, 2005. "Using the Penalized Likelihood Method for Model Selection with Nuisance Parameters Present only under the Alternative: An Application to Switching Regression Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 715-741, September.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:5:p:715-741
    DOI: 10.1111/j.1467-9892.2005.00443.x
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    1. Anna Conte & John D. Hey, 2018. "Assessing multiple prior models of behaviour under ambiguity," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 7, pages 169-188, World Scientific Publishing Co. Pte. Ltd..
    2. Preminger, Arie & Franck, Raphael, 2007. "Forecasting exchange rates: A robust regression approach," International Journal of Forecasting, Elsevier, vol. 23(1), pages 71-84.
    3. PREMINGER, Arie & HAFNER, Christian, 2006. "Deciding between GARCH and stochastic volatility via strong decision rules," LIDAM Discussion Papers CORE 2006042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Jiménez-Gamero, M.D. & Pino-Mejías, R. & Alba-Fernández, V. & Moreno-Rebollo, J.L., 2011. "Minimum [phi]-divergence estimation in misspecified multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3365-3378, December.
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