Finite Sample Breakdown of $M$- and $P$-Estimators

Variance Breakdown of Huber ( M ) - estimators : n / p → m ∈ ( 1 , ∞ )

Huber’s gross-errors contamination model considers the class Fε of all noise distributions F = (1 − ε)Φ + εH, with Φ standard normal, ε ∈ (0, 1) the contamination fraction, and H the contaminating distribution. A half century ago, Huber evaluated the minimax asymptotic variance in scalar location estimation, min ψ max F∈Fε V (ψ, F ) = 1 I(F ∗ ε ) (1) where V (ψ,F ) denotes the asymptotic varian...

Multivariate Location Estimators with the Best Possible Finite Sample Breakdown

The sample mean has long been used as an estimator of a location pa rameter in statistical data analysis and inference Though attractive from many viewpoints it su ers from an extreme sensitivity to outliers The median has been adopted as a more robust location estimator in one dimension it will not break down even if up to half of the data points are bad Another desirable property of the media...

An Alternative Definition of Finite Sample Breakdown Point with Applications to Regression Model Estimators

Finite sample properties of multiple imputation estimators

Finite sample properties of multiple imputation estimators under the linear regression model are studied. The exact bias of the multiple imputation variance estimator is presented. A method of reducing the bias is presented and simulation is used to make comparisons. We also show that the suggested method can be used for a general class of linear estimators. 1. Introduction. Multiple imputation...

Computation of the Finite Sample Risk of M-Estimators on Neighborhoods

We compare various approaches for the determination of finite sample risks of one-dimensional location M-estimators on convex-contaminationand total-variation-type neighborhoods. As risks we consider MSE and certain over-/ undershooting probabilities like in Huber (1968) and Rieder (1980). These methods include (numerically) exact formulae (via FFT, Kohl et al. (2005)), Edgeworth expansions, sa...