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标准化影响矩阵及其应用AI 解读

In this article we introduce the standardized influence matrix (SIM) of parameter estimators as a conjugate of the sample covariance matrix of standardized influence functions (SIFs) evaluated at the data points. We propose principal component analysis for the SIM and its complement (SIM analysis) as a diagnostic tool for regression or other statistical inference, and provide theoretical insight to the local influence defined by Cook. We show that SIM analysis reveals the…

球面与欧氏空间中刚体运动的M估计AI 解读

This paper calculates the influence functions and asymptotic distributions of $M$-estimators of the rotation $A$ in a spherical regression model on the unit sphere in $p$ dimensions with isotropic errors. The problem arises in the reconstruction of the motion of a rigid body on the surface of the sphere. The comparable model for $p$-dimensional Euclidean space data is that $(\nu_1, \ldots, \nu_n)$ are independent with $\nu_i$ symmetrically distributed around $\gamma A \cdot u_i + b, u_i$…

von Mises–Fisher 分布集中参数的稳健估计AI 解读

We introduce a simple procedure for obtaining robust estimates of the concentration parameter of the von Mises-Fisher distribution on the $q$-dimensional unit sphere. The procedure is based on the median deviation from a location parameter. Its influence function is derived and standardized bias robustness is proved. The asymptotic efficiency is calculated and an example is given.

方向数据估计量的稳健性AI 解读

Some standard robustness concepts, developed for linear data, are found wanting in the case of directional data. We introduce a standardized bias robustness allowing for uniform robustness considerations of statistics for bounded parameter spaces. Specifically, we verify the nonrobustness in this sense of the directional mean, the directional dispersion and the maximum likelihood estimator of the concentration parameter of the von Mises-Fisher distributions.