Robust nonparametric inference for the median

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 measures of robustness and efficiency under contamination for confidence intervals and tests. These measures are computed for the proposed procedures. © Institute of Mathematical Statistics, 2004

Combining locally and globally robust estimates for regression

A new class of estimates for the linear model is introduced. These estimates, that we call C-estimates, are defined as a convex combination of a high breakdown point estimate, T1, and any other estimate, T2. We prove that C-estimates retain the global robustness properties of T1 and inherit the local robustness behavior and the asymptotic distribution of T2. In particular, a C-estimate will have an asymptotic normal distribution and bounded contamination sensitivity if T2 does. We also present an estimate with the maximum breakdown point and as efficient as the least squares estimate for normal errors. The maximum bias under outliers contamination of these estimates is computed for different fractions of contamination, and a Monte Carlo study is performed to asses the robustness and efficiency properties of the proposed estimates for finite sample size

Combining locally and globally robust estimates for regression

A new class of estimates for the linear model is introduced. These estimates, that we call C-estimates, are defined as a convex combination of a high breakdown point estimate, T1, and any other estimate, T2. We prove that C-estimates retain the global robustness properties of T1 and inherit the local robustness behavior and the asymptotic distribution of T2. In particular, a C-estimate will have an asymptotic normal distribution and bounded contamination sensitivity if T2 does. We also present an estimate with the maximum breakdown point and as efficient as the least squares estimate for normal errors. The maximum bias under outliers contamination of these estimates is computed for different fractions of contamination, and a Monte Carlo study is performed to asses the robustness and efficiency properties of the proposed estimates for finite sample size

Robust estimators of accelerated failure time regression with generalized log-gamma errors

The generalized log-gamma (GLG) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology. Estimators are proposed which are simultaneously highly robust and highly efficient for the parameters of a GLG distribution in the presence of censoring. Estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the GLG family are also introduced. It is proven that the proposed estimators are asymptotically fully efficient and the maximum mean square error is examined using Monte Carlo simulations. The simulations confirm that the proposed estimators are highly robust and highly efficient for a finite sample size. Finally, the benefits of the proposed estimators in applications are illustrated with the help of two real datasets

A goodness-of-fit test based on ranks for arma models

Available from Centro de Informacion y Documentacion Cientifica CINDOC. Joaquin Costa, 22. 28002 Madrid. SPAIN / CINDOC - Centro de Informaciòn y Documentaciòn CientìficaSIGLEESSpai

A Robust Probabilistic Estimation Framework for Parametric Image Models

Abstract. Models of spatial variation in images are central to a large number of low-level computer vision problems including segmentation, registration, and 3D structure detection. Often, images are represented using parametric models to characterize (noise-free) image variation, and, additive noise. However, the noise model may be unknown and parametric models may only be valid on individual segments of the image. Consequently, we model noise using a nonparametric kernel density estimation framework and use a locally or globally linear parametric model to represent the noise-free image pattern. This results in a novel, robust, redescending, M- parameter estimator for the above image model which we call the Kernel Maximum Likelihood estimator (KML). We also provide a provably convergent, iterative algorithm for the resultant optimization problem. The estimation framework is empirically validated on synthetic data and applied to the task of range image segmentation.