OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.<br /

Robust multivariate methods in Chemometrics

This chapter presents an introduction to robust statistics with applications of a chemometric nature. Following a description of the basic ideas and concepts behind robust statistics, including how robust estimators can be conceived, the chapter builds up to the construction (and use) of robust alternatives for some methods for multivariate analysis frequently used in chemometrics, such as principal component analysis and partial least squares. The chapter then provides an insight into how these robust methods can be used or extended to classification. To conclude, the issue of validation of the results is being addressed: it is shown how uncertainty statements associated with robust estimates, can be obtained.Comment: This article is an update of: P. Filzmoser, S. Serneels, R. Maronna, P.J. Van Espen, 3.24 - Robust Multivariate Methods in Chemometrics, in Comprehensive Chemometrics, 1st Edition, edited by Steven D. Brown, Rom\'a Tauler, Beata Walczak, Elsevier, 2009, https://doi.org/10.1016/B978-044452701-1.00113-

High-Breakdown Robust Multivariate Methods

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that are robust against the possibility that one or several unannounced outliers may occur anywhere in the data. These methods then allow to detect outlying observations by their residuals from a robust fit. We focus on high-breakdown methods, which can deal with a substantial fraction of outliers in the data. We give an overview of recent high-breakdown robust methods for multivariate settings such as covariance estimation, multiple and multivariate regression, discriminant analysis, principal components and multivariate calibration.Comment: Published in at http://dx.doi.org/10.1214/088342307000000087 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Robustness and Outliers

Producción CientíficaUnexpected deviations from assumed models as well as the presence of certain amounts of outlying data are common in most practical statistical applications. This fact could lead to undesirable solutions when applying non-robust statistical techniques. This is often the case in cluster analysis, too. The search for homogeneous groups with large heterogeneity between them can be spoiled due to the lack of robustness of standard clustering methods. For instance, the presence of (even few) outlying observations may result in heterogeneous clusters artificially joined together or in the detection of spurious clusters merely made up of outlying observations. In this chapter we will analyze the effects of different kinds of outlying data in cluster analysis and explore several alternative methodologies designed to avoid or minimize their undesirable effects.Ministerio de Economía, Industria y Competitividad (MTM2014-56235-C2-1-P)Junta de Castilla y León (programa de apoyo a proyectos de investigación – Ref. VA212U13

Robust and Regularized Algorithms for Vehicle Tractive Force Prediction and Mass Estimation

This work provides novel robust and regularized algorithms for parameter estimation with applications in vehicle tractive force prediction and mass estimation. Given a large record of real world data from test runs on public roads, recursive algorithms adjusted the unknown vehicle parameters under a broad variation of statistical assumptions for two linear gray-box models

Uncertainty modelling in power system state estimation

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.As a special case of the static state estimation problem, the load-flow problem is studied in this thesis. It is demonstrated that the non-linear load-flow formulation may be solved by real-coded genetic algorithms. Due to its global optimisation ability, the proposed method can be useful for off-line studies where multiple solutions are suspected. This thesis presents two methods for estimating the uncertainty interval in power system state estimation due to uncertainty in the measurements. The proposed formulations are based on a parametric approach which takes in account the meter inaccuracies. A nonlinear and a linear formulation are proposed to estimate the tightest possible upper and lower bounds on the states. The uncertainty analysis, in power system state estimation, is also extended to other physical quantities such as the network parameters. The uncertainty is then assumed to be present in both measurements and network parameters. To find the tightest possible upper and lower bounds of any state variable, the problem is solved by a Sequential Quadratic Programming (SQP) technique. A new robust estimator based on the concept of uncertainty in the measurements is developed here. This estimator is known as Maximum Constraints Satisfaction (MCS). Robustness and performance of the proposed estimator is analysed via simulation of simple regression examples, D.C. and A.C. power system models.Embassy of Kuwai