IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/93400.html

Monotonic Estimation for Probability Distribution and Multivariate Risk Scales by Constrained Minimum Generalized Cross-Entropy

Author

Listed:
  • Yang, Bill Huajian

Abstract

Minimum cross-entropy estimation is an extension to the maximum likelihood estimation for multinomial probabilities. Given a probability distribution {r_i }_(i=1)^k, we show in this paper that the monotonic estimates {p_i }_(i=1)^k for the probability distribution by minimum cross-entropy are each given by the simple average of the given distribution values over some consecutive indexes. Results extend to the monotonic estimation for multivariate outcomes by generalized cross-entropy. These estimates are the exact solution for the corresponding constrained optimization and coincide with the monotonic estimates by least squares. A non-parametric algorithm for the exact solution is proposed. The algorithm is compared to the “pool adjacent violators” algorithm in least squares case for the isotonic regression problem. Applications to monotonic estimation of migration matrices and risk scales for multivariate outcomes are discussed.

Suggested Citation

  • Yang, Bill Huajian, 2019. "Monotonic Estimation for Probability Distribution and Multivariate Risk Scales by Constrained Minimum Generalized Cross-Entropy," MPRA Paper 93400, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:93400
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/93400/1/MPRA_paper_93400.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Potharst, R. & Feelders, A.J., 2002. "Classification Trees for Problems with Monotonicity Constraints," ERIM Report Series Research in Management ERS-2002-45-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    2. de Leeuw, Jan & Hornik, Kurt & Mair, Patrick, 2009. "Isotone Optimization in R: Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i05).
    3. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    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. Yang, Bill Huajian, 2019. "Resolutions to flip-over credit risk and beyond," MPRA Paper 93389, University Library of Munich, Germany.
    2. Kearney, Fearghal & Shang, Han Lin & Sheenan, Lisa, 2019. "Implied volatility surface predictability: The case of commodity markets," Journal of Banking & Finance, Elsevier, vol. 108(C).
    3. Eric Hillebrand & Huiyu Huang & Tae-Hwy Lee & Canlin Li, 2018. "Using the Entire Yield Curve in Forecasting Output and Inflation," Econometrics, MDPI, vol. 6(3), pages 1-27, August.
    4. Matsumura, Marco & Moreira, Ajax & Vicente, José, 2011. "Forecasting the yield curve with linear factor models," International Review of Financial Analysis, Elsevier, vol. 20(5), pages 237-243.
    5. Lin, Bing-Huei, 1999. "Fitting the term structure of interest rates for Taiwanese government bonds," Journal of Multinational Financial Management, Elsevier, vol. 9(3-4), pages 331-352, November.
    6. Plat, Richard, 2009. "Stochastic portfolio specific mortality and the quantification of mortality basis risk," Insurance: Mathematics and Economics, Elsevier, vol. 45(1), pages 123-132, August.
    7. Lily Y. Liu, 2017. "Estimating Loss Given Default from CDS under Weak Identification," Supervisory Research and Analysis Working Papers RPA 17-1, Federal Reserve Bank of Boston.
    8. Chiarella, Carl & Kang, Boda & Nikitopoulos, Christina Sklibosios & Tô, Thuy-Duong, 2013. "Humps in the volatility structure of the crude oil futures market: New evidence," Energy Economics, Elsevier, vol. 40(C), pages 989-1000.
    9. Sergio Zúñiga, 1999. "Modelos de Tasas de Interés en Chile: Una Revisión," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 36(108), pages 875-893.
    10. Detlefsen, Kai & Härdle, Wolfgang Karl, 2006. "Forecasting the term structure of variance swaps," SFB 649 Discussion Papers 2006-052, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    11. Evangelos Salachas & Georgios P. Kouretas & Nikiforos T. Laopodis, 2024. "The term structure of interest rates and economic activity: Evidence from the COVID‐19 pandemic," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 43(4), pages 1018-1041, July.
    12. Mehmet Pasaogullari & Simeon Tsonevy, 2011. "The term structure of inflation compensation in the nominal yield curve," Working Papers (Old Series) 1133, Federal Reserve Bank of Cleveland.
    13. Pongsak Luangaram & Yuthana Sethapramote, 2016. "Central Bank Communication and Monetary Policy Effectiveness: Evidence from Thailand," PIER Discussion Papers 20, Puey Ungphakorn Institute for Economic Research.
    14. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    15. Victor Lapshin, 2019. "A Nonparametric Approach to Bond Portfolio Immunization," Mathematics, MDPI, vol. 7(11), pages 1-12, November.
    16. Esteban Méndez-Chacón & Diana Van Patten, 2022. "Voting on a Trade Agreement: Firm Networks and Attitudes Toward Openness," Documentos de Trabajo 2204, Banco Central de Costa Rica.
    17. repec:hum:wpaper:sfb649dp2017-027 is not listed on IDEAS
    18. Pagliari, Maria Sole, 2024. "Does one (unconventional) size fit all? Effects of the ECB’s unconventional monetary policies on the euro area economies," European Economic Review, Elsevier, vol. 168(C).
    19. Gary S. Anderson & Alena Audzeyeva, 2019. "A Coherent Framework for Predicting Emerging Market Credit Spreads with Support Vector Regression," Finance and Economics Discussion Series 2019-074, Board of Governors of the Federal Reserve System (U.S.).
    20. João Frois Caldeira & Rangan Gupta & Muhammad Tahir Suleman & Hudson S. Torrent, 2021. "Forecasting the Term Structure of Interest Rates of the BRICS: Evidence from a Nonparametric Functional Data Analysis," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 57(15), pages 4312-4329, December.
    21. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:93400. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.