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

Alfonso García-Pérez ()
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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

Mathematics, 2023, vol. 11, issue 12, 1-13

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.

Keywords: robust statistics; von Mises expansions; saddlepoint approximations; Mendelian randomization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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