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多个异常值的识别AI 解读

One approach to identifying outliers is to assume that the outliers have a different distribution from the remaining observations. In this article we define outliers in terms of their position relative to the model for the good observations. The outlier identification problem is then the problem of identifying those observations that lie in a so-called outlier region. Methods based on robust statistics and outward testing are shown to have the highest possible breakdown…

Rousseeuw 最小体积椭球估计量的渐近性质AI 解读

Rousseeuw's minimum volume estimator for multivariate location and dispersion parameters has the highest possible breakdown point for an affine equivariant estimator. In this paper we establish that it satisfies a local Holder condition of order $1/2$ and converges weakly at the rate of $n^{-1/3}$ to a non-Gaussian distribution.

线性回归模型中S估计量的渐近性质AI 解读

We consider the consistency and weak convergence of $S$-estimators in the linear regression model. Sufficient conditions for consistency with varying dimension are given which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carriers. A weak convergence theorem for the Hampel-Rousseeuw least median of squares estimator is obtained, and it is shown under rather general conditions that the correct norming factor is $n^{1/3}$. Finally, the asymptotic…