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Victor J. Yohai

Publications and source records attributed to Victor J. Yohai.

15 recordsLinked to original sources
arXiv2025

Forecasting High Dimensional Time Series with Dynamic Dimension Reduction

Many dimension reduction techniques have been developed for independent data, and most have also been extended to time series. However, these methods often fail to account for the dynamic dependencies both within and across series. In this work, we propose a general framework for forecasting high-dimensional time series that integrates dynamic dimension reduction with regularization techniques. The effectiveness of the proposed approach is illustrated through a simulated example and a forecasting application using an economic dataset. We show that several specific methods are encompassed within this framework, including Dynamic Principal Components and Reduced Rank Autoregressive Models. Furthermore, time-domain formulations of Dynamic Canonical Correlation and Dynamic Redundancy Analysis are introduced here for the first time as particular instances of the proposed methodology. All of these techniques are analyzed as special cases of a unified procedure, enabling a coherent derivation and interpretation across methods.

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arXiv2021

Robust Model-Based Clustering

We propose a new class of robust and Fisher-consistent estimators for mixture models. These estimators can be used to construct robust model-based clustering procedures. We study in detail the case of multivariate normal mixtures and propose a procedure that uses S estimators of multivariate location and scatter. We develop an algorithm to compute the estimators and to build the clusters which is quite similar to the EM algorithm. An extensive Monte Carlo simulation study shows that our proposal compares favorably with other robust and non robust model-based clustering procedures. We apply ours and alternative procedures to a real data set and again find that the best results are obtained using our proposal.

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arXiv2019

Optimal robust estimators for families of distributions on the integers

Let F_{θ} be a family of distributions with support on the set of nonnegative integers Z_0. In this paper we derive the M-estimators with smallest gross error sensitivity (GES). We start by defining the uniform median of a distribution F with support on Z_0 (umed(F)) as the median of x+u, where x and u are independent variables with distributions F and uniform in [-0.5,0.5] respectively. Under some general conditions we prove that the estimator with smallest GES satisfies umed(F_{n})=umed(F_{θ}), where F_{n} is the empirical distribution. The asymptotic distribution of these estimators is found. This distribution is normal except when there is a positive integer k so that F_{θ}(k)=0.5. In this last case, the asymptotic distribution behaves as normal at each side of 0, but with different variances. A simulation Monte Carlo study compares, for the Poisson distribution, the efficiency and robustness for finite sample sizes of this estimator with those of other robust estimators.

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arXiv2019

Robust Clustering Using Tau-Scales

K means is a popular non-parametric clustering procedure introduced by Steinhaus (1956) and further developed by MacQueen (1967). It is known, however, that K means does not perform well in the presence of outliers. Cuesta-Albertos et al (1997) introduced a robust alternative, trimmed K means, which can be tuned to be robust or efficient, but cannot achieve these two properties simultaneously in an adaptive way. To overcome this limitation we propose a new robust clustering procedure called K Tau Centers, which is based on the concept of Tau scale introduced by Yohai and Zamar (1988). We show that K Tau Centers performs well in extensive simulation studies and real data examples. We also show that the centers found by the proposed method are consistent estimators of the "true" centers defined as the minimizers of the the objective function at the population level.

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arXiv2017

Robust Estimation in High Dimensional Generalized Linear Models

Generalized Linear Models are routinely used in data analysis. The classical procedures for estimation are based on Maximum Likelihood and it is well known that the presence of outliers can have a large impact on this estimator. Robust procedures are presented in the literature but they need a robust initial estimate in order to be computed. This is especially important for robust procedures with non convex loss function such as redescending M-estimators. Subsampling techniques are often used to determine a robust initial estimate; however when the number of unknown parameters is large the number of subsamples needed in order to have a high probability of having one subsample free of outliers become infeasible. Furthermore the subsampling procedure provides a non deterministic starting point. Based on ideas in Pena and Yohai (1999), we introduce a deterministic robust initial estimate for M-estimators based on transformations Valdora and Yohai (2014) for which we also develop an iteratively reweighted least squares algorithm. The new methods are studied by Monte Carlo experiments.

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arXiv2017

Forecasting Multiple Time Series with One-Sided Dynamic Principal Components

We define one-sided dynamic principal components (ODPC) for time series as linear combinations of the present and past values of the series that minimize the reconstruction mean squared error. Previous definitions of dynamic principal components depend on past and future values of the series. For this reason, they are not appropriate for forecasting purposes. On the contrary, it is shown that the ODPC introduced in this paper can be successfully used for forecasting high-dimensional multiple time series. An alternating least squares algorithm to compute the proposed ODPC is presented. We prove that for stationary and ergodic time series the estimated values converge to their population analogues. We also prove that asymptotically, when both the number of series and the sample size go to infinity, if the data follows a dynamic factor model, the reconstruction obtained with ODPC converges, in mean squared error, to the common part of the factor model. Monte Carlo results shows that forecasts obtained by the ODPC compare favourably with other forecasting methods based on dynamic factor models.

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arXiv2016

Multivariate Location and Scatter Matrix Estimation Under Cellwise and Casewise Contamination

We consider the problem of multivariate location and scatter matrix estimation when the data contain cellwise and casewise outliers. Agostinelli et al. (2015) propose a two-step approach to deal with this problem: first, apply a univariate filter to remove cellwise outliers and second, apply a generalized S-estimator to downweight casewise outliers. We improve this proposal in three main directions. First, we introduce a consistent bivariate filter to be used in combination with the univariate filter in the first step. Second, we propose a new fast subsampling procedure to generate starting points for the generalized S-estimator in the second step. Third, we consider a non-monotonic weight function for the generalized S-estimator to better deal with casewise outliers in high dimension. A simulation study and real data example show that, unlike the original two-step procedure, the modified two-step approach performs and scales well for high dimension. Moreover, the modified procedure outperforms the original one and other state-of-the-art robust procedures under cellwise and casewise data contamination.

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arXiv2015

Robust estimators of accelerated failure time regression with generalized log-gamma errors

The generalized log-gamma (GLG) model is a very flexible family of distributions to analyze datasets in many different areas of science and technology. In this paper, we propose estimators which are simultaneously highly robust and highly efficient for the parameters of a GLG distribution in the presence of censoring. We also introduced estimators with the same properties for accelerated failure time models with censored observations and error distribution belonging to the GLG family. We prove that the proposed estimators are asymptotically fully efficient and examine the maximum mean square error using Monte Carlo simulations. The simulations confirm that the proposed estimators are highly robust and highly efficient for finite sample size. Finally, we illustrate the good behavior of the proposed estimators with two real datasets.

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arXiv2015

Robust and efficient estimation of high dimensional scatter and location

We deal with the equivariant estimation of scatter and location for p-dimensional data, giving emphasis to scatter. It it important that the estimators possess both a high efficiency for normal data and a high resistance to outliers, that is, a low bias under contamination. The most frequently employed estimators are not quite satisfactory in this respect. The Minimum Volume Ellipsoid (MVE) and Minimum Covariance Determinant (MCD) estimators are known to have a very low efficiency. S-Estimators (Davies 1987) with a monotonic weight function like the bisquare behave satisfactorily for "small" p, say p not larger than 10. Rocke (1996) showed that their efficiency tends to one with increasing p. Unfortunately, this advantage is paid with a serious loss of robustness for large p. We consider three families of estimators with controllable efficiencies: non-monotonic S-estimators (Rocke 1996), MM-estimators (Tatsuoka and Tyler 2000) and tau-estimators (Lopuhaa 1991), whose performance for large p has not been explored to date. Two types of starting estimators are employed: the MVE computed through subsampling, and a semi-deterministic procedure proposed by Peña and Prieto (2007) for outlier detection. A simulation study shows that the Rocke and MM estimators starting from the Peña-Prieto estimator and with an adequate tuning, can simultaneously attain high efficiency and high robustness.

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arXiv2014

Composite Robust Estimators for Linear Mixed Models

The Classical Tukey-Huber Contamination Model (CCM) is a usual framework to describe the mechanism of outliers generation in robust statistics. In a data set with $n$ observations and $p$ variables, under the CCM, an outlier is a unit, even if only one or few values are corrupted. Classical robust procedures were designed to cope with this setting and the impact of observations were limited whenever necessary. Recently, a different mechanism of outliers generation, namely Independent Contamination Model (ICM), was introduced. In this new setting each cell of the data matrix might be corrupted or not with a probability independent on the status of the other cells. ICM poses new challenge to robust statistics since the percentage of contaminated rows dramatically increase with $p$, often reaching more than $50\%$. When this situation appears, classical affine equivariant robust procedures do not work since their breakdown point is $50\%$. For this contamination model we propose a new type of robust methods namely composite robust procedures which are inspired on the idea of composite likelihood, where low dimension likelihood, very often the likelihood of pairs, are aggregate together in order to obtain an approximation of the full likelihood which is more tractable. Our composite robust procedures are build over pairs of observations in order to gain robustness in the independent contamination model. We propose composite S and $τ$-estimators for linear mixed models. Composite $τ$-estimators are proved to have an high breakdown point both in the CCM and ICM. A Monte Carlo study shows that our estimators compare favorably with respect to classical S-estimators under the CCM and outperform them under the ICM. One example based on a real data set illustrates the new robust procedure.

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arXiv2014

Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination

Multivariate location and scatter matrix estimation is a cornerstone in multivariate data analysis. We consider this problem when the data may contain independent cellwise and casewise outliers. Flat data sets with a large number of variables and a relatively small number of cases are common place in modern statistical applications. In these cases global down-weighting of an entire case, as performed by traditional robust procedures, may lead to poor results. We highlight the need for a new generation of robust estimators that can efficiently deal with cellwise outliers and at the same time show good performance under casewise outliers.

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arXiv2010

Robust location estimation with missing data

In a missing-data setting, we have a sample in which a vector of explanatory variables x_i is observed for every subject i, while scalar outcomes y_i are missing by happenstance on some individuals. In this work we propose robust estimates of the distribution of the responses assuming missing at random (MAR) data, under a semiparametric regression model. Our approach allows the consistent estimation of any weakly continuous functional of the response's distribution. In particular, strongly consistent estimates of any continuous location functional, such as the median or MM functionals, are proposed. A robust fit for the regression model combined with the robust properties of the location functional gives rise to a robust recipe for estimating the location parameter. Robustness is quantified through the breakdown point of the proposed procedure. The asymptotic distribution of the location estimates is also derived.

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arXiv2009

Propagation of outliers in multivariate data

We investigate the performance of robust estimates of multivariate location under nonstandard data contamination models such as componentwise outliers (i.e., contamination in each variable is independent from the other variables). This model brings up a possible new source of statistical error that we call "propagation of outliers." This source of error is unusual in the sense that it is generated by the data processing itself and takes place after the data has been collected. We define and derive the influence function of robust multivariate location estimates under flexible contamination models and use it to investigate the effect of propagation of outliers. Furthermore, we show that standard high-breakdown affine equivariant estimators propagate outliers and therefore show poor breakdown behavior under componentwise contamination when the dimension $d$ is high.

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arXiv2005

Robust nonparametric inference for the median

We consider the problem of constructing robust nonparametric confidence intervals and tests of hypothesis for the median when the data distribution is unknown and the data may contain a small fraction of contamination. We propose a modification of the sign test (and its associated confidence interval) which attains the nominal significance level (probability coverage) for any distribution in the contamination neighborhood of a continuous distribution. We also define some measures of robustness and efficiency under contamination for confidence intervals and tests. These measures are computed for the proposed procedures.

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