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A New Estimator: Median of the Distribution of the Mean in Robustness

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  • Alfonso García-Pérez

    (Departamento de Estadística, I.O. y C.N., Universidad Nacional de Educación a Distancia (UNED), Paseo Senda del Rey 9, 28040 Madrid, Spain)

Abstract

In some statistical methods, the statistical information is provided in terms of the values used by classical estimators, such as the sample mean and sample variance. These estimations are used in a second stage, usually in a classical manner, to be combined into a single value, as a weighted mean. Moreover, in many applied studies, the results are given in these terms, i.e., as summary data. In all of these cases, the individual observations are unknown; therefore, computing the usual robustness estimators with them to replace classical non-robust estimations by robust ones is not possible. In this paper, the use of the median of the distribution F x ¯ of the sample mean is proposed, assuming a location-scale contaminated normal model, where the parameters of F x ¯ are estimated with the classical estimations provided in the first stage. The estimator so defined is called median of the distribution of the mean, M d M . This new estimator is applied in Mendelian randomization, defining the new robust inverse weighted estimator, RIVW.

Suggested Citation

  • Alfonso García-Pérez, 2023. "A New Estimator: Median of the Distribution of the Mean in Robustness," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2694-:d:1170608
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    References listed on IDEAS

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    1. Ronchetti, Elvezio, 2020. "Accurate and robust inference," Econometrics and Statistics, Elsevier, vol. 14(C), pages 74-88.
    2. Rodriguez, Daniela & Valdora, Marina, 2019. "The breakdown point of the median of means tournament," Statistics & Probability Letters, Elsevier, vol. 153(C), pages 108-112.
    3. Pires, Ana M. & Branco, João A., 2002. "Partial Influence Functions," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 451-468, November.
    4. K. E. Basford & G. J. McLachlan, 1985. "Likelihood Estimation with Normal Mixture Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(3), pages 282-289, November.
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