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von Mises–Fisher 分布方向参数的中位数型估计AI 解读

We study three median-type estimators of direction: the normalized spatial median, L1-estimator on the sphere and spherical median. Their asymptotic distributions, efficiencies, influence functions and sensitivities are given at the von Mises-Fisher model. A simulation study is also carried out to compare their finite sample performance in terms of mean squared errors. We conclude that overall the normalized spatial median is the preferred estimator.

重新加权最小二乘估计量与初始估计量具有相同收敛率AI 解读

The problem of combining high efficiency with high breakdown properties for regression estimators has piqued the interest of statisticians for some time. One proposal specifically suggested by Rousseeuw and Leroy is to use the least median of squares estimator, omit observations whose residuals are larger than some constant cut-off value and apply least squares to the remaining observations. Although this proposal does retain high breakdown point, it actually converges no…

回归估计量的尾部行为及其崩溃点AI 解读

A measure of finite sample estimator performance based on the probability of large deviations is introduced. The tail performance of the least squares estimator is studied in detail, and the authors find that it achieves good tail performance under strictly Gaussian conditions, but performance is extremely poor in the case of heavy-tailed error distributions. Turning to the tail behavior of various robust estimators, they focus on tail performance under heavy (algebraic)…

统计检验的崩溃稳健性AI 解读

Power and level breakdown functions of a test statistic are introduced to obtain a unified analysis of local stability (as typified by the influence function) and global stability (as illustrated by the breakdown point). The power breakdown function gives the amount of contamination of each alternative distribution that can carry the test statistic to a null value. The level breakdown function gives the amount of contamination of a null distribution that can carry the test…