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M-estimators for Models with a Mix of Discrete and Continuous Parameters

Author

Listed:
  • Ting Fung Ma

    (University of South Carolina)

  • Juan Francisco Mandujano Reyes

    (University of Wisconsin-Madison)

  • Jun Zhu

    (University of Wisconsin-Madison)

Abstract

A variety of parametric models are specified by a mix of discrete parameters, which take values from a countable set, and continuous parameters, which take values from a continuous space. However, the asymptotic properties of the parameter estimators are not well understood in the literature. In this paper, we consider the general framework of M-estimation and derive the asymptotic properties of the M-estimators of both discrete and continuous parameters. In particular, we show that the M-estimators are consistent and the continuous parameters are asymptotically normal. We also extend a large deviation principle from models with only discrete parameters to models with discrete and continuous parameters. The finite-sample properties are assessed by a simulation study, and for illustration, we perform a break-point analysis for the clinical outcomes of COVID-19 patients.

Suggested Citation

  • Ting Fung Ma & Juan Francisco Mandujano Reyes & Jun Zhu, 2024. "M-estimators for Models with a Mix of Discrete and Continuous Parameters," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 164-190, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00317-7
    DOI: 10.1007/s13171-023-00317-7
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    References listed on IDEAS

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    1. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, September.
    2. James O. Berger & Jose M. Bernardo & Dongchu Sun, 2012. "Objective Priors for Discrete Parameter Spaces," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 636-648, June.
    3. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.
    4. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    5. Friedrich Liese & Igor Vajda, 1995. "Necessary and sufficient conditions for consistency of generalizedM-estimates," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 42(1), pages 291-324, December.
    6. Jenish, Nazgul & Prucha, Ingmar R., 2012. "On spatial processes and asymptotic inference under near-epoch dependence," Journal of Econometrics, Elsevier, vol. 170(1), pages 178-190.
    7. Yuan, Ke-Hai & Jennrich, Robert I., 1998. "Asymptotics of Estimating Equations under Natural Conditions," Journal of Multivariate Analysis, Elsevier, vol. 65(2), pages 245-260, May.
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