IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v55y2011i12p3365-3378.html
   My bibliography  Save this article

Minimum [phi]-divergence estimation in misspecified multinomial models

Author

Listed:
  • Jiménez-Gamero, M.D.
  • Pino-Mejías, R.
  • Alba-Fernández, V.
  • Moreno-Rebollo, J.L.

Abstract

The consequences of model misspecification for multinomial data when using minimum [phi]-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:12:p:3365-3378
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947311002520
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Kim, Sung-Ho & Choi, Hyemi & Lee, Sangjin, 2009. "Estimate-based goodness-of-fit test for large sparse multinomial distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1122-1131, February.
    2. Basu, Ayenendranath & Sarkar, Sahadeb, 1994. "On disparity based goodness-of-fit tests for multinomial models," Statistics & Probability Letters, Elsevier, vol. 19(4), pages 307-312, March.
    3. Vuong, Quang H, 1989. "Likelihood Ratio Tests for Model Selection and Non-nested Hypotheses," Econometrica, Econometric Society, vol. 57(2), pages 307-333, March.
    4. Hidetoshi Shimodaira, 1998. "An Application of Multiple Comparison Techniques to Model Selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 1-13, March.
    5. Vuong, Quang H. & Wang, Weiren, 1993. "Minimum chi-square estimation and tests for model selection," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 141-168, March.
    6. 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.
    7. Wang, Yong, 2007. "Minimum disparity computation via the iteratively reweighted least integrated squares algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5662-5672, August.
    8. Granger, Clive W. J. & King, Maxwell L. & White, Halbert, 1995. "Comments on testing economic theories and the use of model selection criteria," Journal of Econometrics, Elsevier, vol. 67(1), pages 173-187, May.
    9. Basu, Ayanendranath & Park, Chanseok & Lindsay, Bruce G. & Li, Haihong, 2004. "Some variants of minimum disparity estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 741-763, May.
    10. Douglas Rivers & Quang Vuong, 2002. "Model selection tests for nonlinear dynamic models," Econometrics Journal, Royal Economic Society, vol. 5(1), pages 1-39, June.
    11. Lee, Sangyeol & Vonta, Ilia & Karagrigoriou, Alex, 2011. "A maximum entropy type test of fit," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2635-2643, September.
    12. Raúl Jiménz & Yongzhao Shao, 2001. "On robustness and efficiency of minimum divergence estimators," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 241-248, December.
    13. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. M. Jiménez-Gamero & A. Batsidis & M. Alba-Fernández, 2016. "Fourier methods for model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 105-133, February.

    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. M. Jiménez-Gamero & R. Pino-Mejías & A. Rufián-Lizana, 2014. "Minimum $$K_{\phi }$$ K ϕ -divergence estimators for multinomial models and applications," Computational Statistics, Springer, vol. 29(1), pages 363-401, February.
    2. M. Jiménez-Gamero & A. Batsidis & M. Alba-Fernández, 2016. "Fourier methods for model selection," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 105-133, February.
    3. Mur, Jesús & Angulo, Ana, 2009. "Model selection strategies in a spatial setting: Some additional results," Regional Science and Urban Economics, Elsevier, vol. 39(2), pages 200-213, March.
    4. In-Koo Cho & Kenneth Kasa, 2015. "Learning and Model Validation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(1), pages 45-82.
    5. Susanne M. Schennach & Daniel Wilhelm, 2017. "A Simple Parametric Model Selection Test," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1663-1674, October.
    6. Chen, Xiaohong & Hong, Han & Shum, Matthew, 2007. "Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models," Journal of Econometrics, Elsevier, vol. 141(1), pages 109-140, November.
    7. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    8. repec:bgu:wpaper:0603 is not listed on IDEAS
    9. Massimiliano Marcellino & Barbara Rossi, 2008. "Model Selection for Nested and Overlapping Nonlinear, Dynamic and Possibly Mis‐specified Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 867-893, December.
    10. 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.
    11. Francesco Bravo, 2022. "Misspecified semiparametric model selection with weakly dependent observations," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(4), pages 558-586, July.
    12. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2015. "Bad environments, good environments: A non-Gaussian asymmetric volatility model," Journal of Econometrics, Elsevier, vol. 186(1), pages 258-275.
    13. R. Golden, 2003. "Discrepancy Risk Model Selection Test theory for comparing possibly misspecified or nonnested models," Psychometrika, Springer;The Psychometric Society, vol. 68(2), pages 229-249, June.
    14. Liu, Tuo & Lee, Lung-fei, 2019. "A likelihood ratio test for spatial model selection," Journal of Econometrics, Elsevier, vol. 213(2), pages 434-458.
    15. Christophe Bontemps & Grayham E. Mizon, 2008. "Encompassing: Concepts and Implementation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(s1), pages 721-750, December.
    16. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
    17. 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).
    18. Gourieroux, C. & Monfort, A., 2021. "Model risk management: Valuation and governance of pseudo-models," Econometrics and Statistics, Elsevier, vol. 17(C), pages 1-22.
    19. Yen, Steven T. & Chern, Wen S. & Lee, Hwang-Jaw, 1991. "Effects Of Income Sources On Household Food Expenditures," 1991 Annual Meeting, August 4-7, Manhattan, Kansas 271167, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    20. Magnus, Jan R., 2007. "The Asymptotic Variance Of The Pseudo Maximum Likelihood Estimator," Econometric Theory, Cambridge University Press, vol. 23(5), pages 1022-1032, October.
    21. Corradi, Valentina & Swanson, Norman R., 2004. "A test for the distributional comparison of simulated and historical data," Economics Letters, Elsevier, vol. 85(2), pages 185-193, November.

    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:eee:csdana:v:55:y:2011:i:12:p:3365-3378. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.