Robust statistics

Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal. Robust statistical methods have been developed for many common problems, such as estimating location, scale and regression parameters. One motivation is to produce statistical methods that are not unduly affected by outliers. Another motivationis to provide methods with good performance when there are small departures from parametric distributions. The book "Robust Statistics" contains eight chapters. We propose a robust level set image segmentation model combining local with global fitting energies to segment noised images in first chapter. Second chapter addresses the robustness of the SCKF filter and tuning parameters of the SCKF, especially for the noise statistical parameters. Third chapter advocates the use of robust statistical procedures for the analysis of HRV times series and proposes the TC-MLqE for time series models. In fourth chapetr, robust neighborhood statistics such as MEDIANI, MADI, and LREIi have been introduced to explore the spatial variation of Fe203, to identify weak anomalies in covered areas, and for comparison with the singularity index. A 3D interactive muti-object segmentation tool using local robust statistics driven active contours has been discussed in fifth chapter. In sixth chapter, we develop an original approach for neural network sequential learning that does not require preprocessing of the data to model and process outliers. We present a robust generalized empirical likelihood estimator and confidence region for the parameters of an autoregression in seventh chapter that have a heavy tailed heteroscedastic error. Robust estimation of precision matrices under cellwise contamination has been introduced in last chapter.