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具有高崩溃点的高效多变量位置估计量AI 解读

We propose an affine equivariant estimator of multivariate location that combines a high breakdown point and a bounded influence function with high asymptotic efficiency. This proposal is basically a location $M$-estimator based on the observations obtained after scaling with an affine equivariant high breakdown covariance estimator. The resulting location estimator will inherit the breakdown point of the initial covariance estimator and within the location-covariance model…

多元位置与协方差矩阵仿射等变估计量的崩溃点AI 解读

Finite-sample replacement breakdown points are derived for different types of estimators of multivariate location and covariance matrices. The role of various equivariance properties is illustrated. The breakdown point is related to a measure of performance based on large deviations probabilities. Finally, we show that one-step reweighting preserves the breakdown point.

多变量位置与协方差的 S 估计和 M 估计之间的关系AI 解读

We discuss the relation between $S$-estimators and $M$-estimators of multivariate location and covariance. As in the case of the estimation of a multiple regression parameter, $S$-estimators are shown to satisfy first-order conditions of $M$-estimators. We show that the influence function IF $(\mathbf{x; S}, F)$ of $S$-functionals exists and is the same as that of corresponding $M$-functionals. Also, we show that $S$-estimators have a limiting normal distribution which is…