WeproposetheuseofarobustcovarianceestimatorbasedonmultivariateWinsorizationinthecontextoftheTarr–... more WeproposetheuseofarobustcovarianceestimatorbasedonmultivariateWinsorizationinthecontextoftheTarr–Müller–WeberframeworkforsparseestimationoftheprecisionmatrixofaGaussiangraphicalmodel.LikewiseCroux–Öllerer’sprecisionmatrixestimator,ourproposedestimatorattainsthemaximumfinite-samplebreakdownpointof0.5undercellwisecontamination.WeconductanextensiveMonteCarlosimulationstudytoassesstheperformanceofoursandthecurrentlyexistingproposals.Wefindthatourshasacompetitivebehavior,regardingtheestimationoftheprecisionmatrixandtherecoveryofthegraph.Wedemonstratetheusefulnessoftheproposedmethodologyinarealapplicationtobreastcancerdata.
Journal of the Royal Statistical Society Series A: Statistics in Society, 2018
SummaryAdministrative data are becoming increasingly important. They are typically the side effec... more SummaryAdministrative data are becoming increasingly important. They are typically the side effect of some operational exercise and are often seen as having significant advantages over alternative sources of data. Although it is true that such data have merits, statisticians should approach the analysis of such data with the same cautious and critical eye as they approach the analysis of data from any other source. The paper identifies some statistical challenges, with the aim of stimulating debate about and improving the analysis of administrative data, and encouraging methodology researchers to explore some of the important statistical problems which arise with such data.
In this paper, a new method for supervised classification of hyperspectral images is proposed for... more In this paper, a new method for supervised classification of hyperspectral images is proposed for the case in which the size of the training sample is small. It consists of replacing in the Mahalanobis distance the maximum likelihood estimator of the precision matrix by a sparse estimator. The method is compared with two other existing versions of \textit{LDA} sparse, both in real and simulated images.
We propose the use of a robust covariance estimator based on multivariate Winsorization in the co... more We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr–Müller–Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux–Öllerer’s precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast
We propose the use of a robust covariance estimator based on multivariate Winsorization in the co... more We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr-Müller-Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux-Öllerer's precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast cancer data.
Journal of Data Science, Statistics, and Visualisation
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit... more We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of the Pearson correlation coefficients between the prediction errors of the nodes’ best linear predictors. We propose a novel stepwise algorithm for detecting pairs of conditionally dependent variables. We compare the proposed algorithm with existing methods including graphical lasso (Glasso), constrained `l1-minimization(CLIME) and equivalent partial correlation (EPC), via simulation studies and real life applications. In our simulation study we consider several model settings and report the results using different performance measures that look at desirable features of the recovered graph.
In this work we study the asymptotic behavior of a robust class of estimators of the coefficient ... more In this work we study the asymptotic behavior of a robust class of estimators of the coefficient of a AR-2D process. We establish the precise conditions for the consistency and asymptotic normality of the RA estimator. The AR-2D model has many applications in image modeling and statistical image processing, therefore the relevance of knowing such properties. The adequacy of the
Journal of Statistical Planning and Inference, 2008
When the data used to fit a nonparametric regression model are contaminated with outliers, we nee... more When the data used to fit a nonparametric regression model are contaminated with outliers, we need to use a robust estimator of scale in order to make robust estimation of the regression function possible. We develop a family of M-estimators of scale constructed from consecutive differences of regression responses. Estimators in our family robustify the estimator proposed by Rice [1984. Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215–1230]. Under appropriate conditions, we establish the weak consistency and asymptotic normality of all estimators in our family. Estimators in our family vary in terms of their robustness properties. We quantify the robustness of each estimator via the maxbias. We use this measure as a basis for deriving the asymptotic breakdown point of the estimator. Our theoretical results allow us to specify conditions for estimators in our family to achieve a maximum asymptotic breakdown point of 12. We conduct a simulation study to compare the finite sample performance of our preferred M-estimator with that of three other estimators.
When the data used to fit an heteroscedastic nonparametric regression model are contaminated with... more When the data used to fit an heteroscedastic nonparametric regression model are contaminated with outliers, robust estimators of the scale function are needed in order to obtain robust estimators of the regression function and to construct robust confidence bands. In this paper, local M-estimators of the scale function based on consecutive differences of the responses, for fixed designs are considered.
WeproposetheuseofarobustcovarianceestimatorbasedonmultivariateWinsorizationinthecontextoftheTarr–... more WeproposetheuseofarobustcovarianceestimatorbasedonmultivariateWinsorizationinthecontextoftheTarr–Müller–WeberframeworkforsparseestimationoftheprecisionmatrixofaGaussiangraphicalmodel.LikewiseCroux–Öllerer’sprecisionmatrixestimator,ourproposedestimatorattainsthemaximumfinite-samplebreakdownpointof0.5undercellwisecontamination.WeconductanextensiveMonteCarlosimulationstudytoassesstheperformanceofoursandthecurrentlyexistingproposals.Wefindthatourshasacompetitivebehavior,regardingtheestimationoftheprecisionmatrixandtherecoveryofthegraph.Wedemonstratetheusefulnessoftheproposedmethodologyinarealapplicationtobreastcancerdata.
Journal of the Royal Statistical Society Series A: Statistics in Society, 2018
SummaryAdministrative data are becoming increasingly important. They are typically the side effec... more SummaryAdministrative data are becoming increasingly important. They are typically the side effect of some operational exercise and are often seen as having significant advantages over alternative sources of data. Although it is true that such data have merits, statisticians should approach the analysis of such data with the same cautious and critical eye as they approach the analysis of data from any other source. The paper identifies some statistical challenges, with the aim of stimulating debate about and improving the analysis of administrative data, and encouraging methodology researchers to explore some of the important statistical problems which arise with such data.
In this paper, a new method for supervised classification of hyperspectral images is proposed for... more In this paper, a new method for supervised classification of hyperspectral images is proposed for the case in which the size of the training sample is small. It consists of replacing in the Mahalanobis distance the maximum likelihood estimator of the precision matrix by a sparse estimator. The method is compared with two other existing versions of \textit{LDA} sparse, both in real and simulated images.
We propose the use of a robust covariance estimator based on multivariate Winsorization in the co... more We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr–Müller–Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux–Öllerer’s precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast
We propose the use of a robust covariance estimator based on multivariate Winsorization in the co... more We propose the use of a robust covariance estimator based on multivariate Winsorization in the context of the Tarr-Müller-Weber framework for sparse estimation of the precision matrix of a Gaussian graphical model. Likewise Croux-Öllerer's precision matrix estimator, our proposed estimator attains the maximum finite sample breakdown point of 0.5 under cellwise contamination. We conduct an extensive Monte Carlo simulation study to assess the performance of ours and the currently existing proposals. We find that ours has a competitive behavior, regarding the the estimation of the precision matrix and the recovery of the graph. We demonstrate the usefulness of the proposed methodology in a real application to breast cancer data.
Journal of Data Science, Statistics, and Visualisation
We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit... more We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of the Pearson correlation coefficients between the prediction errors of the nodes’ best linear predictors. We propose a novel stepwise algorithm for detecting pairs of conditionally dependent variables. We compare the proposed algorithm with existing methods including graphical lasso (Glasso), constrained `l1-minimization(CLIME) and equivalent partial correlation (EPC), via simulation studies and real life applications. In our simulation study we consider several model settings and report the results using different performance measures that look at desirable features of the recovered graph.
In this work we study the asymptotic behavior of a robust class of estimators of the coefficient ... more In this work we study the asymptotic behavior of a robust class of estimators of the coefficient of a AR-2D process. We establish the precise conditions for the consistency and asymptotic normality of the RA estimator. The AR-2D model has many applications in image modeling and statistical image processing, therefore the relevance of knowing such properties. The adequacy of the
Journal of Statistical Planning and Inference, 2008
When the data used to fit a nonparametric regression model are contaminated with outliers, we nee... more When the data used to fit a nonparametric regression model are contaminated with outliers, we need to use a robust estimator of scale in order to make robust estimation of the regression function possible. We develop a family of M-estimators of scale constructed from consecutive differences of regression responses. Estimators in our family robustify the estimator proposed by Rice [1984. Bandwidth choice for nonparametric regression. Ann. Statist. 12, 1215–1230]. Under appropriate conditions, we establish the weak consistency and asymptotic normality of all estimators in our family. Estimators in our family vary in terms of their robustness properties. We quantify the robustness of each estimator via the maxbias. We use this measure as a basis for deriving the asymptotic breakdown point of the estimator. Our theoretical results allow us to specify conditions for estimators in our family to achieve a maximum asymptotic breakdown point of 12. We conduct a simulation study to compare the finite sample performance of our preferred M-estimator with that of three other estimators.
When the data used to fit an heteroscedastic nonparametric regression model are contaminated with... more When the data used to fit an heteroscedastic nonparametric regression model are contaminated with outliers, robust estimators of the scale function are needed in order to obtain robust estimators of the regression function and to construct robust confidence bands. In this paper, local M-estimators of the scale function based on consecutive differences of the responses, for fixed designs are considered.
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Papers by Marcelo Ruiz