Influence Functions of the Spearman and Kendall Correlation Measures

Mathematics Subject Classification (2000) 62G35 · 62F99

Estimators of the multiple correlation coefficient: local robustness and confidence intervals.

Many robust regression estimators are defined by minimizing a measure of spread of the residuals. An accompanying R-2-measure, or multiple correlation coefficient, is then easily obtained. In this paper, local robustness properties of these robust R-2-coefficients axe investigated. It is also shown how confidence intervals for the population multiple correlation coefficient can be constructed in the case of multivariate normality.Cautionary note; High breakdown-point; Influence function; Intervals; Model; Multiple correlation coefficient; R-2-measure; Regression analysis; Residuals; Robustness; Squares regression;

The K-Step Spatial Sign Covariance Matrix

The Sign Covariance Matrix is an orthogonal equivariant estimator of mul- tivariate scale. It is often used as an easy-to-compute and highly robust estimator. In this paper we propose a k-step version of the Sign Covariance Matrix, which improves its e±ciency while keeping the maximal breakdown point. If k tends to infinity, Tyler's M-estimator is obtained. It turns out that even for very low values of k, one gets almost the same e±ciency as Tyler's M-estimator.

Robust Estimation of Mean and Dispersion Functions in Extended Generalized Additive Models

Generalized Linear Models are a widely used method to obtain parametric es- timates for the mean function. They have been further extended to allow the re- lationship between the mean function and the covariates to be more flexible via Generalized Additive Models. However the fixed variance structure can in many cases be too restrictive. The Extended Quasi-Likelihood (EQL) framework allows for estimation of both the mean and the dispersion/variance as functions of covari- ates. As for other maximum likelihood methods though, EQL estimates are not resistant to outliers: we need methods to obtain robust estimates for both the mean and the dispersion function. In this paper we obtain functional estimates for the mean and the dispersion that are both robust and smooth. The performance of the proposed method is illustrated via a simulation study and some real data examples.dispersion;generalized additive modelling;mean regression function;quasilikelihood;M-estimation;P-splines;robust estimation

The breakdown behavior of the maximum likelihood estimator in the logistic regression model.

In this note we discuss the breakdown behavior of the maximum likelihood (ML) estimator in the logistic regression model. We formally prove that the ML-estimator never explodes to infinity, but rather breaks down to zero when adding severe outliers to a data set. An example confirms this behavior. (C) 2002 Published by Elsevier Science B.V.breakdown point; logistic regression; maximum likelihood; robust estimation; generalized linear-models; robustness; existence; fits;

Robust Forecasting of Non-Stationary Time Series

This paper proposes a robust forecasting method for non-stationary time series. The time series is modelled using non-parametric heteroscedastic regression, and fitted by a localized MM-estimator, combining high robustness and large efficiency. The proposed method is shown to produce reliable forecasts in the presence of outliers, non-linearity, and heteroscedasticity. In the absence of outliers, the forecasts are only slightly less precise than those based on a localized Least Squares estimator. An additional advantage of the MM-estimator is that it provides a robust estimate of the local variability of the time series.Heteroscedasticity;Non-parametric regression;Prediction;Outliers;Robustness