论文检索

线性混合模型的复合稳健估计量AI 解读

The classical Tukey–Huber contamination model (CCM) is a commonly adopted framework to describe the mechanism of outliers generation in robust statistics. Given a dataset with n observations and p variables, under the CCM, an outlier is a unit, even if only one or a few values are corrupted. Classical robust procedures were designed to cope with this type of outliers. Recently, a new mechanism of outlier generation was introduced, namely, the independent contamination model…

缺失数据下多元位置与散布的稳健估计AI 解读

Two main issues regarding data quality are data contamination (outliers) and data completion (missing data). These two problems have attracted much attention and research but surprisingly, they are seldom considered together. Popular robust methods such as S-estimators of multivariate location and scatter offer protection against outliers but cannot deal with missing data, except for the obviously inefficient approach of deleting all incomplete cases. We generalize the…

ARMA 模型的稳健估计AI 解读

This paper introduces a new class of robust estimates for ARMA models. They are M-estimates, but the residuals are computed so the effect of one outlier is limited to the period where it occurs. These estimates are closely related to those based on a robust filter, but they have two important advantages: they are consistent and the asymptotic theory is tractable. We perform a Monte Carlo where we show that these estimates compare favorably with respect to standard…

删失数据的高崩溃点稳健回归AI 解读

In this paper, we propose a class of high breakdown point estimators for the linear regression model when the response variable contains censored observations. These estimators are robust against high-leverage outliers and they generalize the LMS (least median of squares), S, MM and τ-estimators for linear regression. An important contribution of this paper is that we can define consistent estimators using a bounded loss function (or equivalently, a redescending score…

中位数的稳健非参数推断AI 解读

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some…

位置参数的最优稳健 M 估计AI 解读

We find optimal robust estimates for the location parameter of n independent measurements from a common distribution F that belongs to a contamination neighborhood of a normal distribution. We follow an asymptotic minimax approach similar to Huber's but work with full neighborhoods of the central parametric model including nonsymmetric distributions. Our optimal estimates minimize monotone functions of the estimate's asymptotic variance and bias, which include asymptotic…

Stahel–Donoho 稳健多元估计量的表现AI 解读

The Stahel-Donoho estimators (t, V) of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w(r), where w is a weight function and r is a measure of “outlyingness,” obtained by considering all univariate projections of the data. It has a high breakdown point for all dimensions and order √n consistency. The asymptotic bias of V for point mass contamination for suitable weight functions is compared with that…