IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v86y2024i1d10.1007_s13171-023-00317-7.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-023-00317-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13171-023-00317-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464, July.
    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. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
    4. 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.
    5. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gabriele Fiorentini & Enrique Sentana, 2021. "Specification tests for non‐Gaussian maximum likelihood estimators," Quantitative Economics, Econometric Society, vol. 12(3), pages 683-742, July.
    2. Tauchen, George E., 1995. "New Minimum Chi-Square Methods in Empirical Finance," Working Papers 95-42, Duke University, Department of Economics.
    3. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
    4. Jun Ishii & Jingming Yan, 2007. "Does divestiture crowd out new investment? The “make or buy” decision in the U.S. electricity generation industry," RAND Journal of Economics, RAND Corporation, vol. 38(1), pages 185-213, March.
    5. Yi-Ting Chen & Zhongjun Qu, 2015. "M Tests with a New Normalization Matrix," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 617-652, May.
    6. Jonas Dovern & Hans Manner, 2020. "Order‐invariant tests for proper calibration of multivariate density forecasts," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 440-456, June.
    7. Tae-Hwy Lee & Zhou Xi & Ru Zhang, 2013. "Testing for Neglected Nonlinearity Using Regularized Artificial Neural Networks," Working Papers 201422, University of California at Riverside, Department of Economics, revised Apr 2012.
    8. Lejeune, Bernard, 2009. "A diagnostic m-test for distributional specification of parametric conditional heteroscedasticity models for financial data," Journal of Empirical Finance, Elsevier, vol. 16(3), pages 507-523, June.
    9. Gallant, A. Ronald & Tauchen, George, 2002. "Simulated Score Methods and Indirect Inference for Continuous-time Models," Working Papers 02-09, Duke University, Department of Economics.
    10. Kline Patrick & Santos Andres, 2012. "A Score Based Approach to Wild Bootstrap Inference," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 23-41, August.
    11. Chen, Yi-Ting, 2012. "A simple approach to standardized-residuals-based higher-moment tests," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 427-453.
    12. Teodosio Pérez Amaral, 1994. "Contrastes de momentos y de la matriz de información," Documentos de Trabajo del ICAE 9401, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    13. Walter Beckert, 2015. "Choice in the Presence of Experts," Birkbeck Working Papers in Economics and Finance 1503, Birkbeck, Department of Economics, Mathematics & Statistics.
    14. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    15. Andrés Langebaek R. & Diego Vásquez E., 2007. "Determinantes de la actividad innovadora en la industria manufacturera colombiana," Borradores de Economia 433, Banco de la Republica de Colombia.
    16. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    17. Coenen, Gunter & Wieland, Volker, 2005. "A small estimated euro area model with rational expectations and nominal rigidities," European Economic Review, Elsevier, vol. 49(5), pages 1081-1104, July.
    18. Guido M. Kuersteiner & Ingmar R. Prucha, 2020. "Dynamic Spatial Panel Models: Networks, Common Shocks, and Sequential Exogeneity," Econometrica, Econometric Society, vol. 88(5), pages 2109-2146, September.
    19. Blasques, Francisco & van Brummelen, Janneke & Gorgi, Paolo & Koopman, Siem Jan, 2024. "Maximum Likelihood Estimation for Non-Stationary Location Models with Mixture of Normal Distributions," Journal of Econometrics, Elsevier, vol. 238(1).
    20. Parente, Paulo M.D.C. & Smith, Richard J., 2011. "Gel Methods For Nonsmooth Moment Indicators," Econometric Theory, Cambridge University Press, vol. 27(1), pages 74-113, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00317-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.