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This revised book provides a thorough explanation of the foundation of robust methods, incorporating the latest updates on R and S-Plus, robust ANOVA (Analysis of Variance) and regression. It guides advanced students and other professionals through the basic strategies used for developing practical solutions to problems, and provides a brief background on the foundations of modern methods, placing the new methods in historical context. Author Rand Wilcox includes chapter exercises and many real-world examples that illustrate how various methods perform in different situations.Introduction to Robust Estimation and Hypothesis Testing, Second Edition, focuses on the practical applications of modern, robust methods which can greatly enhance our chances of detecting true differences among groups and true associations among variables. * Covers latest developments in robust regression* Covers latest improvements in ANOVA* Includes newest rank-based methods* Describes and illustrated easy to use software

Gelernte Klassifikationsverfahren sind nicht sicher, wenn Angreifer gezielte Veränderungen an der Eingabe vornehmen. Obwohl diese Änderungen für den Menschen kaum wahrnehmbar sind, ändert sich die Klassifikation. Um gelernte Modelle in sicherheitskritischen Bereichen anwenden zu können, ist es erforderlich, Methoden zu entwickeln, die Robustheit gegen adversariale Angriffe gewährleisten können. Hier wird eine Übersicht über verschiedene Anwendungsfälle, Angriffe, die daraus entstehenden Problemstellungen, Ansätze zur Verteidigung sowie Gefahren bei der Evaluation dieser gegeben und die Notwendigkeit korrekter Verfahren aufgezeigt.

Many traditional methods for identifying changepoints can struggle in the presence of outliers, or when the noise is heavy-tailed. Often they will infer additional changepoints to fit the outliers. To overcome this problem, data often needs to be preprocessed to remove outliers, though this is difficult for applications where the data needs to be analyzed online. We present an approach to changepoint detection that is robust to the presence of outliers. The idea is to adapt existing penalized cost approaches for detecting changes so that they use loss functions that are less sensitive to outliers. We argue that loss functions that are bounded, such as the classical biweight loss, are particularly suitable-as we show that only bounded loss functions are robust to arbitrarily extreme outliers. We present an efficient dynamic programming algorithm that can find the optimal segmentation under our penalized cost criteria. Importantly, this algorithm can be used in settings where the data needs to be analyzed online. We show that we can consistently estimate the number of changepoints, and accurately estimate their locations, using the biweight loss function. We demonstrate the usefulness of our approach for applications such as analyzing well-log data, detecting copy number variation, and detecting tampering of wireless devices. Supplementary materials for this article are available online.

This paper introduces a simple principle for robust statistical inference via appropriate shrinkage on the data. This widens the scope of high-dimensional techniques, reducing the distributional conditions from subexponential or sub-Gaussian to more relaxed bounded second or fourth moment. As an illustration of this principle, we focus on robust estimation of the low-rank matrix Θ* from the trace regression model Y = Tr(Θ*TX) + ε. It encompasses four popular problems: sparse linear model, compressed sensing, matrix completion and multitask learning. We propose to apply the penalized least-squares approach to the appropriately truncated or shrunk data. Under only bounded 2 + δ moment condition on the response, the proposed robust methodology yields an estimator that possesses the same statistical error rates as previous literature with sub-Gaussian errors. For sparse linear model and multitask regression, we further allow the design to have only bounded fourth moment and obtain the same statistical rates. As a byproduct, we give a robust covariance estimator with concentration inequality and optimal rate of convergence in terms of the spectral norm, when the samples only bear bounded fourth moment. This result is of its own interest and importance. We reveal that under high dimensions, the sample covariance matrix is not optimal whereas our proposed robust covariance can achieve optimality. Extensive simulations are carried out to support the theories.

A preeminent expert in the field explores new and exciting methodologies in the ever-growing field of robust statistics Used to develop data analytical methods, which are resistant to outlying observations in the data, while capable of detecting outliers, robust statistics is extremely useful for solving an array of common problems, such as estimating location, scale, and regression parameters. Written by an internationally recognized expert in the field of robust statistics, this book addresses a range of well-established techniques while exploring, in depth, new and exciting methodologies. Local robustness and global robustness are discussed, and problems of non-identifiability and adaptive estimation are considered. Rather than attempt an exhaustive investigation of robustness, the author provides readers with a timely review of many of the most important problems in statistical inference involving robust estimation, along with a brief look at confidence intervals for location. Throughout, the author meticulously links research in maximum likelihood estimation with the more general M-estimation methodology. Specific applications and R and some MATLAB subroutines with accompanying data sets—available both in the text and online—are employed wherever appropriate. Providing invaluable insights and guidance, Robustness Theory and Application: * Offers a balanced presentation of theory and applications within each topic-specific discussion * Features solved examples throughout which help clarify complex and/or difficult concepts * Meticulously links research in maximum likelihood type estimation with the more general M-estimation methodology * Delves into new methodologies which have been developed over the past decade without stinting on coverage of \"tried-and-true\" methodologies * Includes R and some MATLAB subroutines with accompanying data sets, which help illustrate the power of the methods described Robustness Theory and Application is an important resource for all statisticians interested in the topic of robust statistics. This book encompasses both past and present research, making it a valuable supplemental text for graduate-level courses in robustness.

In this paper we focus on robust linear optimization problems with uncertainty regions defined by φ -divergences (for example, chi-squared, Hellinger, Kullback-Leibler). We show how uncertainty regions based on φ -divergences arise in a natural way as confidence sets if the uncertain parameters contain elements of a probability vector. Such problems frequently occur in, for example, optimization problems in inventory control or finance that involve terms containing moments of random variables, expected utility, etc. We show that the robust counterpart of a linear optimization problem with φ -divergence uncertainty is tractable for most of the choices of φ typically considered in the literature. We extend the results to problems that are nonlinear in the optimization variables. Several applications, including an asset pricing example and a numerical multi-item newsvendor example, illustrate the relevance of the proposed approach. This paper was accepted by Gérard P. Cachon, optimization.

We study the phenomenon of business ecosystems in which platform firms orchestrate the functioning of ecosystems by providing platforms and setting the rules for participation by complementor firms. We develop a theoretical framework to explain how the structural and evolutionary features of the ecosystem may shape the extent to which participating complementor firms can sustain their superior performance. The structural feature, which we refer to as ecosystem complexity, is a function of the number of unique components or subsystems that interact with the complementor’s product. We incorporate the evolutionary features by considering the role of generational transitions initiated by platform firms over time as well as the role of complementors’ ecosystem-specific experience. Evidence from Apple’s iOS and Google’s Android smartphone ecosystems supports our arguments that higher ecosystem complexity helps app developers sustain their superior performance, and that this effect is stronger for more experienced firms. In contrast, platform transitions initiated by Apple and Google make it more difficult for app developers to sustain their performance superiority, and that this effect is exacerbated by the extent of ecosystem complexity. The study offers a novel account of how the performance of complementor firms in platform-based business ecosystems may be shaped by their ecosystem-level interdependencies.

We propose a semiparametric approach called the nonparanormal SKEPTIC for efficiently and robustly estimating high-dimensional undirected graphical models. To achieve modeling flexibility, we consider the nonparanormal graphical models proposed by Liu, Lafferty and Wasserman [J. Mach. Learn. Res. 10 (2009) 2295-2328]. To achieve estimation robustness, we exploit nonparametric rank-based correlation coefficient estimators, including Spearman's rho and Kendall's tau. We prove that the nonparanormal SKEPTIC achieves the optimal parametric rates of convergence for both graph recovery and parameter estimation. This result suggests that the nonparanormal graphical models can be used as a safe replacement of the popular Gaussian graphical models, even when the data are truly Gaussian. Besides theoretical analysis, we also conduct thorough numerical simulations to compare the graph recovery performance of different estimators under both ideal and noisy settings. The proposed methods are then applied on a large-scale genomic data set to illustrate their empirical usefulness. The R package huge implementing the proposed methods is available on the Comprehensive R Archive Network: http://cran.r-project.org/.

Electroencephalography (EEG), magnetoencephalography (MEG) and related techniques are prone to glitches, slow drift, steps, etc., that contaminate the data and interfere with the analysis and interpretation. These artifacts are usually addressed in a preprocessing phase that attempts to remove them or minimize their impact. This paper offers a set of useful techniques for this purpose: robust detrending, robust rereferencing, outlier detection, data interpolation (inpainting), step removal, and filter ringing artifact removal. These techniques provide a less wasteful alternative to discarding corrupted trials or channels, and they are relatively immune to artifacts that disrupt alternative approaches such as filtering. Robust detrending allows slow drifts and common mode signals to be factored out while avoiding the deleterious effects of glitches. Robust rereferencing reduces the impact of artifacts on the reference. Inpainting allows corrupt data to be interpolated from intact parts based on the correlation structure estimated over the intact parts. Outlier detection allows the corrupt parts to be identified. Step removal fixes the high-amplitude flux jump artifacts that are common with some MEG systems. Ringing removal allows the ringing response of the antialiasing filter to glitches (steps, pulses) to be suppressed. The performance of the methods is illustrated and evaluated using synthetic data and data from real EEG and MEG systems. These methods, which are mainly automatic and require little tuning, can greatly improve the quality of the data. •Preprocessing is essential for EEG and MEG data analysis.•Robust methods for data preprocessing are not affected by glitches and artifacts.•Methods include robust detrending, rereferencing, inpainting and step removal.•These methods are effective and complementary with standard techniques such as ICA.

We consider the problem of robustly predicting as well as the best linear combination of d given functions in least squares regression, and variants of this problem including constraints on the parameters of the linear combination. For the ridge estimator and the ordinary least squares estimator, and their variants, we provide new risk bounds of order d/n without logarithmic factor unlike some standard results, where n is the size of the training data. We also provide a new estimator with better deviations in the presence of heavy-tailed noise. It is based on truncating differences of losses in a min-max framework and satisfies a d/n risk bound both in expectation and in deviations. The key common surprising factor of these results is the absence of exponential moment condition on the output distribution while achieving exponential deviations. All risk bounds are obtained through a PAC-Bayesian analysis on truncated differences of losses. Experimental results strongly back up our truncated min-max estimator.