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Robust Nonparametric Inference for the Multivariate Trimmed Mean

Makhtar Sarr

Abstract



Univariate trimmed means are among the most popular estimators of location parameters but their extension to higher dimensions is not trivial. Several multivariate trimmed means using different depth functions can be compared based on their performance but there seems to be a gap between sound theory and computational feasibility. This paper introduces multivariate trimmed means based on spherical data depth measures with an order of computation growing linearly in the dimension of the data. A new winsorization method will be introduced to estimate the α-trimmed mean and its covariance matrix, to construct confidence regions based on the α-trimmed mean, and to test hypotheses using α-trimmed Hotelling tests statistic. Results are based on simulation studies for uncontaminated as well as contaminated data. Applications to real data will be discussed and future research directions addressed.

Keywords


Trimming, winsorizing, affine equivariancy, invariancy, and robustness.

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