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Maximum entropy principle and statistical inference on condensed ordered data

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  • 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
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    References listed on IDEAS

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    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.

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