IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/93400.html
   My bibliography  Save this paper

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. 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.
    3. 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).
    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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Dick Dijk & Siem Jan Koopman & Michel Wel & Jonathan H. Wright, 2014. "Forecasting interest rates with shifting endpoints," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(5), pages 693-712, August.
    8. 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.).
    9. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    10. 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.
    11. Nguyen, Minh, 2020. "Collateral haircuts and bond yields in the European government bond markets," International Review of Financial Analysis, Elsevier, vol. 69(C).
    12. Adam Traczyk, 2013. "Financial integration and the term structure of interest rates," Empirical Economics, Springer, vol. 45(3), pages 1267-1305, December.
    13. John Y. Campbell & Glen B. Taksler, 2003. "Equity Volatility and Corporate Bond Yields," Journal of Finance, American Finance Association, vol. 58(6), pages 2321-2350, December.
    14. Chamon, Marcos & Schumacher, Julian & Trebesch, Christoph, 2018. "Foreign-Law Bonds: Can They Reduce Sovereign Borrowing Costs?," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 114, pages 164-179.
    15. 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.
    16. Ang, Andrew & Piazzesi, Monika & Wei, Min, 2006. "What does the yield curve tell us about GDP growth?," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 359-403.
    17. Shigenori Shiratsuka, 2021. "Monetary Policy Effectiveness under the Ultra-Low Interest Rate Environment: Evidence from Yield Curve Dynamics in Japan," Keio-IES Discussion Paper Series 2021-012, Institute for Economics Studies, Keio University.
    18. Hong, Zhiwu & Niu, Linlin & Zhang, Chen, 2022. "Affine arbitrage-free yield net models with application to the euro debt crisis," Journal of Econometrics, Elsevier, vol. 230(1), pages 201-220.
    19. Rui Hua & Wenzhe Hu & Xiuju Zhao, 2020. "Research on RMB exchange rate forecast based on the neural network model and the Nelson–Siegel model," Risk Management, Palgrave Macmillan, vol. 22(3), pages 219-237, September.
    20. Venetis, Ioannis & Ladas, Avgoustinos, 2022. "Co-movement and global factors in sovereign bond yields," MPRA Paper 115801, University Library of Munich, Germany.

    More about this item

    Keywords

    maximum likelihood; cross-entropy; least squares; isotonic regression; constrained optimization; multivariate risk scales;
    All these 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.