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Estimators of parameters of a mixture of three multinomial distributions based on simple majority results

Author

Listed:
  • Ricardo Saldanha Morais

    (Federal University of Minas Gerais)

  • Roberto da Costa Quinino

    (Federal University of Minas Gerais)

  • Emilio Suyama

    (Federal University of Minas Gerais)

  • Linda Lee Ho

    (University of São Paulo)

Abstract

For assessing the precision of measurement systems that classify items dichotomically with the possibility of repeated ratings, the maximum likelihood method is commonly used to evaluate misclassification probabilities. However, a computationally simpler and more intuitive approach is the method of simple majority. In this approach, each item is labelled as conforming if the majority of repeated classification outcomes are conforming. A previous study has indicated that this technique yields estimators that have a lower mean squared error than but the same asymptotic properties as the corresponding maximum likelihood estimators. However, there are circumstances in which the use of measurement systems with a wider scale of responses is necessary. In this paper, we propose estimators based on simple majority results for evaluating the classification errors of measurement systems that rate items in a trichotomous domain. We investigate their properties and compare their performance with that of maximum likelihood estimators. We focus on the context in which the true quality states of the objects cannot be determined. The simple majority procedure is modelled using a mixture of three multinomial distributions. The proposed estimators are shown to be a competitive alternative because they offer closed-form expressions and demonstrate a performance similar to that of maximum likelihood estimators.

Suggested Citation

  • Ricardo Saldanha Morais & Roberto da Costa Quinino & Emilio Suyama & Linda Lee Ho, 2019. "Estimators of parameters of a mixture of three multinomial distributions based on simple majority results," Statistical Papers, Springer, vol. 60(4), pages 1283-1316, August.
  • Handle: RePEc:spr:stpapr:v:60:y:2019:i:4:d:10.1007_s00362-017-0875-y
    DOI: 10.1007/s00362-017-0875-y
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    References listed on IDEAS

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    1. de Mast, Jeroen, 2007. "Agreement and Kappa-Type Indices," The American Statistician, American Statistical Association, vol. 61, pages 148-153, May.
    2. Hironori Fujisawa & Shizue Izumi, 2000. "Inference about Misclassification Probabilities from Repeated Binary Responses," Biometrics, The International Biometric Society, vol. 56(3), pages 706-711, September.
    3. Roberto Quinino & Linda Ho & Emílio Suyama, 2013. "Alternative estimator for the parameters of a mixture of two binomial distributions," Statistical Papers, Springer, vol. 54(1), pages 47-69, February.
    4. Norman L. Johnson & Samuel Kotz, 1988. "Estimation from binomial data with classifiers of known and unknown imperfections," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 147-156, February.
    5. T. Pham-Gia & N. Turkhan, 2005. "Bayesian decision criteria in the presence of noises under quadratic and absolute value loss functions," Statistical Papers, Springer, vol. 46(2), pages 247-266, April.
    6. Jian Li & Fugee Tsung & Changliang Zou, 2014. "Multivariate binomial/multinomial control chart," IISE Transactions, Taylor & Francis Journals, vol. 46(5), pages 526-542.
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