IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v34y1997i1p85-93.html
   My bibliography  Save this article

Maximum entropy principle and statistical inference on condensed ordered data

Author

Listed:
  • Menéndez, M.
  • Morales, D.
  • Pardo, L.

Abstract

Using sample quantiles, a point estimation procedure based on the maximum entropy principle is proposed. Under standard regularity conditions it is shown that these estimators are efficient and asymptotically normal. A goodness-of-fit test statistic is also given and its asymptotic chi-square distribution is calculated. The testing mechanism has the advantage with respect to the usual chi-square goodness-of-fit test that it is possible to avoid the difficulties of choosing cell boundaries for grouping.

Suggested Citation

  • Menéndez, M. & Morales, D. & Pardo, L., 1997. "Maximum entropy principle and statistical inference on condensed ordered data," Statistics & Probability Letters, Elsevier, vol. 34(1), pages 85-93, May.
    • Handle: RePEc:eee:stapro:v:34:y:1997:i:1:p:85-93
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(96)00169-1
    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. S. Jammalamadaka & Xian Zhou & Ram Tiwari, 1989. "Asymptotic efficiencies of spacings tests for goodness of fit," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 36(1), pages 355-377, December.
    2. Theil, Henri & O'Brien, Patricia C., 1980. "The median of the maximum entropy distribution," Economics Letters, Elsevier, vol. 5(4), pages 345-347.
    3. Theil, Henri, 1980. "The entropy of the maximum entropy distribution," Economics Letters, Elsevier, vol. 5(2), pages 145-148.
    4. Theil, Henri & Lightburn, Richard O., 1981. "The positive maximum entropy distribution," Economics Letters, Elsevier, vol. 8(1), pages 67-72.
    5. Theil, Henri & Kidwai, Sartaj A., 1981. "Moments of the maximum entropy and the symmetric maximum entropy distribution," Economics Letters, Elsevier, vol. 7(4), pages 349-353.
    6. Theil, Henri & Kidwai, Sartaj A., 1981. "Another look at the maximum entropy correlation coefficient," Economics Letters, Elsevier, vol. 8(2), pages 147-152.
    7. Ebrahimi, Nader & Pflughoeft, Kurt & Soofi, Ehsan S., 1994. "Two measures of sample entropy," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 225-234, June.
    8. Rodriguez, Carlos C. & Van Ryzin, John, 1985. "Maximum entropy histograms," Statistics & Probability Letters, Elsevier, vol. 3(3), pages 117-120, June.
    9. Hall, Peter, 1986. "On powerful distributional tests based on sample spacings," Journal of Multivariate Analysis, Elsevier, vol. 19(2), pages 201-224, August.
    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. G. Aulogiaris & K. Zografos, 2004. "A maximum entropy characterization of symmetric Kotz type and Burr multivariate distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(1), pages 65-83, June.
    2. M. Ekström & S. M. Mirakhmedov & S. Rao Jammalamadaka, 2020. "A class of asymptotically efficient estimators based on sample spacings," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(3), pages 617-636, September.
    3. M. Menéndez & D. Morales & L. Pardo & I. Vajda, 2001. "Minimum Divergence Estimators Based on Grouped Data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 277-288, June.
    4. Bassetti, Federico & Bodini, Antonella & Regazzini, Eugenio, 2007. "Consistency of minimum divergence estimators based on grouped data," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 937-941, June.
    5. Arjun Gupta & Solomon Harrar & Leandro Pardo, 2007. "On testing homogeneity of variances for nonnormal models using entropy," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(2), pages 245-261, August.

    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. Penrose, Mathew D., 2000. "Central limit theorems for k-nearest neighbour distances," Stochastic Processes and their Applications, Elsevier, vol. 85(2), pages 295-320, February.
    2. Soofi, E. S. & Retzer, J. J., 2002. "Information indices: unification and applications," Journal of Econometrics, Elsevier, vol. 107(1-2), pages 17-40, March.
    3. B. Bhargavarama Sarma & B. Shoba, 2022. "Consistent estimation in measurement error models with near singular covariance," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 32-48, March.
    4. Wen Chen & Jinjie Wang & Jianli Ding & Xiangyu Ge & Lijing Han & Shaofeng Qin, 2023. "Detecting Long-Term Series Eco-Environmental Quality Changes and Driving Factors Using the Remote Sensing Ecological Index with Salinity Adaptability (RSEI SI ): A Case Study in the Tarim River Basin,," Land, MDPI, vol. 12(7), pages 1-23, June.
    5. World Bank Group, 2015. "FYR Macedonia Public Expenditure Review," World Bank Publications - Reports 23808, The World Bank Group.
    6. Park, Sangun & Rao, Murali & Shin, Dong Wan, 2012. "On cumulative residual Kullback–Leibler information," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2025-2032.
    7. Sherzod Mirakhmedov & Syed Tirmizi & Muhammad Naeem, 2011. "A Cramér-type large deviation theorem for sums of functions of higher order non-overlapping spacings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 74(1), pages 33-54, July.
    8. Sangun Park & Johan Lim, 2015. "On censored cumulative residual Kullback–Leibler information and goodness-of-fit test with type II censored data," Statistical Papers, Springer, vol. 56(1), pages 247-256, February.
    9. Jan G. De Gooijer & Ao Yuan, 2008. "MDL Mean Function Selection in Semiparametric Kernel Regression Models," Tinbergen Institute Discussion Papers 08-046/4, Tinbergen Institute.
    10. Guoxin Qiu & Kai Jia, 2018. "Extropy estimators with applications in testing uniformity," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 30(1), pages 182-196, January.
    11. Ao Yuan, 2009. "Semiparametric inference with kernel likelihood," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(2), pages 207-228.
    12. Hino, Hideitsu & Koshijima, Kensuke & Murata, Noboru, 2015. "Non-parametric entropy estimators based on simple linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 72-84.
    13. Nader Ebrahimi, 2001. "Testing for Uniformity of the Residual Life Time Based on Dynamic Kullback-Leibler Information," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(2), pages 325-337, June.
    14. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    15. Jan Rosenzweig, 2023. "A Tale of Tail Covariances (and Diversified Tails)," Papers 2302.13646, arXiv.org.
    16. Abo-Eleneen, Z.A. & Almohaimeed, B. & Ng, H.K.T., 2018. "On cumulative residual entropy of progressively censored order statistics," Statistics & Probability Letters, Elsevier, vol. 139(C), pages 47-52.
    17. repec:mse:cesdoc:15045 is not listed on IDEAS
    18. Nelly Litvak & Maria Vlasiou, 2010. "A survey on performance analysis of warehouse carousel systems," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(4), pages 401-447, November.
    19. Reschenhofer, Erhard, 1997. "Generalization of the Kolmogorov-Smirnov test," Computational Statistics & Data Analysis, Elsevier, vol. 24(4), pages 433-441, June.
    20. Huffer, Fred W. & Chien-Tai Lin, 1997. "Computing the exact distribution of the extremes of sums of consecutive spacings," Computational Statistics & Data Analysis, Elsevier, vol. 26(2), pages 117-132, December.
    21. Clément Goulet & Dominique Guegan & Philippe De Peretti, 2015. "Empirical probability density function of Lyapunov exponents," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01167097, HAL.

    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:stapro:v:34:y:1997:i:1:p:85-93. 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/wps/find/journaldescription.cws_home/622892/description#description .

    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.