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Divergence-based estimation and testing with misclassified data

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Abstract

The well-known chi-squared goodness-of-fit test for a multinomial distribution is generally biased when the observations are subject to misclassification. In Pardo and Zografos (2000) the problem was considered using a double sampling scheme and ø-divergence test statistics. A new problem appears if the null hypothesis is not simple because it is necessary to give estimators for the unknown parameters. In this paper the minimum ø-divergence estimators are considered and some of their properties are established. The proposed ø-divergence test statistics are obtained by calculating ø-divergences between probability density functions and by replacing parameters by their minimum ø-divergence estimators in the derived expressions. Asymptotic distributions of the new test statistics are also obtained. The testing procedure is illustrated with an example.

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Authors and Affiliations

  1. Department of Statistics & O. R., Complutense University of Madrid, Madrid

    E. Landaburu & L. Pardo

  2. Operations Research Center, Miguel Hernández University of Elche, Elche

    D. Morales

Authors
  1. E. Landaburu
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  2. D. Morales
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  3. L. Pardo
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Supported by the grant BMF2000-0800.

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Landaburu, E., Morales, D. & Pardo, L. Divergence-based estimation and testing with misclassified data. Statistical Papers 46, 397–409 (2005). https://doi.org/10.1007/BF02762841

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  • DOI: https://doi.org/10.1007/BF02762841

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