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Correspondence analysis is a method for the visual display of information from two-way contingency tables. We introduce a robust form of correspondence analysis based on minimum covariance determinant estimation. This leads to the systematic deletion of outlying rows of the table and to plots of greatly increased informativeness. Our examples are trade flows of clothes and consumer evaluations of the perceived properties of cars. The robust method requires that a specified proportion of the data be used in fitting. To accommodate this requirement we provide an algorithm that uses a subset of complete rows and one row partially, both sets of rows being chosen robustly. We prove the convergence of this algorithm.

The aim of this research is testing a new statistical model able to describe the interaction between soil and atmosphere. The model is based on a robust parametric LTS (Least Trimmed Squares) method and harmonic functions. It has been developed taking into account field measurements of quantities involved in both infiltration and evapo-transpiration phenomena, such as volumetric water content, soil-water potential, air temperature, rainfall amounts and solar radiation. The proposed statistical model allows assessing the volumetric water content at different sites using only time series of daily rainfall amount as input data. The model was applied in different test sites, whose data were assumed by the International Soil Moisture Network (ISMN). In fact, ISMN allows getting free time series of soil and meteorological data from monitoring stations all over the world. This note shows how the proposed model is accurate with respect to field data in estimating the volumetric water content in different soils, climates and depths. Future implications of this research will regard water content predictions, especially in areas where field data are scarce. Since the proposed LTS algorithm is very efficient and the computational workload is rather low, the possibility of coupling it with a slope stability analysis over large areas will be investigated, in order to get a distributed real-time model for shallow landslides susceptibility.

The paper introduces an automatic procedure for the parametric transformation of the response in regression models to approximate normality. We consider the Box–Cox transformation and its generalization to the extended Yeo–Johnson transformation which allows for both positive and negative responses. A simulation study illuminates the superior comparative properties of our automatic procedure for the Box–Cox transformation. The usefulness of our procedure is demonstrated on four sets of data, two including negative observations. An important theoretical development is an extension of the Bayesian Information Criterion (BIC) to the comparison of models following the deletion of observations, the number deleted here depending on the transformation parameter.

Outliers can have a major effect on the estimated transformation of the response in linear regression models, as they can on the estimates of the coefficients of the fitted model. The effect is more extreme in the Generalized Additive Models (GAMs) that are the subject of this article, as the forms of terms in the model can also be affected. We develop, describe and illustrate robust methods for the nonparametric transformation of the response and estimation of the terms in the model. Numerical integration is used to calculate the estimated variance stabilizing transformation. Robust regression provides outlier free input to the polynomial smoothers used in the calculation of the response transformation and in the backfitting algorithm for estimation of the functions of the GAM. Our starting point was the AVAS (Additivity and VAriance Stabilization) algorithm of Tibshirani. Even if robustness is not required, we have made four further general optional improvements to AVAS which greatly improve the performance of Tibshirani’s original Fortran program. We provide a publicly available and fully documented interactive program for our procedure which is a robust form of Tibshirani’s AVAS that allows many forms of robust regression. We illustrate the efficacy of our procedure through data analyses. A refinement of the backfitting algorithm has interesting implications for robust model selection. Supplementary materials for this article are available online.

Asymptotic properties of robust regression estimators are well known. However, it is not always clear what is the best strategy for confidence intervals and hypothesis testing when the sample size is not very large, since the distribution of residuals coming from robust estimates has unknown properties for small samples. In the present work we propose an analysis of various strategies for estimating the variance-covariance matrix of the S estimators at the variation of n and p, considering different �� functions. An adaptive correction strategy is proposed. In addition to the simulation study, an example on a benchmark dataset is shown.

The purpose of this paper is to show in regression clustering how to choose the most relevant solutions, analyze their stability, and provide information about best combinations of optimal number of groups, restriction factor among the error variance across groups and level of trimming. The procedure is based on two steps. First we generalize the information criteria of constrained robust multivariate clustering to the case of clustering weighted models. Differently from the traditional approaches which are based on the choice of the best solution found minimizing an information criterion (i.e. BIC), we concentrate our attention on the so called optimal stable solutions. In the second step, using the monitoring approach, we select the best value of the trimming factor. Finally, we validate the solution using a confirmatory forward search approach. A motivating example based on a novel dataset concerning the European Union trade of face masks shows the limitations of the current existing procedures. The suggested approach is initially applied to a set of well known datasets in the literature of robust regression clustering. Then, we focus our attention on a set of international trade datasets and we provide a novel informative way of updating the subset in the random start approach. The Supplementary material, in the spirit of the Special Issue, deepens the analysis of trade data and compares the suggested approach with the existing ones available in the literature.

Information criteria for model choice are extended to the detection of outliers in regression models. For deletion of observations (hard trimming) the family of models is generated by monitoring properties of the fitted models as the trimming level is varied. For soft trimming (downweighting of observations), some properties are monitored as the efficiency or breakdown point of the robust regression is varied. Least Trimmed Squares and the Forward Search are used to monitor hard trimming, with MM- and S-estimation the methods for soft trimming. Bayesian Information Criteria (BIC) for both scenarios are developed and results about their asymptotic properties provided. In agreement with the theory, simulations and data analyses show good performance for the hard trimming methods for outlier detection. Importantly, this is achieved very simply, without the need to specify either significance levels or decision rules for multiple outliers.

According to Eurostat, the EU production of chemicals hazardous to health reached 211 million tonnes in 2019. Thus, the possibility that some of these chemical compounds interact negatively with the human endocrine system has received, especially in the last decade, considerable attention from the scientific community. It is obvious that given the large number of chemical compounds it is impossible to use in vitro/in vivo tests for identifying all the possible toxic interactions of these chemicals and their metabolites. In addition, the poor availability of highly curated databases from which to retrieve and download the chemical, structure, and regulative information about all food contact chemicals has delayed the application of in silico methods. To overcome these problems, in this study we use robust computational approaches, based on a combination of highly curated databases and molecular docking, in order to screen all food contact chemicals against the nuclear receptor family in a cost and time-effective manner.

Starting with 2020 volume, the journal Metron has decided to celebrate the centenary since its foundation with three special issues. This volume is dedicated to robust statistics. A striking feature of most applied statistical analyses is the use of methods that are well known to be sensitive to outliers or to other departures from the postulated model. Robust statistical methods provide useful tools for reducing this sensitivity, through the detection of the outliers by first fitting the majority of the data and then by flagging deviant data points. The six papers in this issue cover a wide orientation in all fields of robustness. This editorial first provides some facts about the history and current state of robust statistics and then summarizes the contents of each paper. ispartof: METRON-INTERNATIONAL JOURNAL OF STATISTICS vol:79 issue:2 pages:121-125 ispartof: location:Italy status: published