Abstract
A method of determining semiparametric robust maximum likelihood estimates for a family of the Tukey distributions is suggested. The method can be used to obtain robust estimates of data comprising not only major, but also minor outliers. It is shown that these estimates converge to the maximum likelihood estimates of semiparametric problems when the fraction and distribution of outliers are unknown. The estimates have been used to process data of minisodar measurements of vertical profiles of the wind velocity components in the ABL comprising a significant fraction of both major and minor outliers. The high efficiency of the suggested estimates is shown on particular examples.
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