José R. Berrendero

Time series clustering based on forecast densities

A new clustering method for time series is proposed, based on the full probability density of the forecasts. First, a resampling method combined with a nonparametric kernel estimator provides estimates of the forecast densities. A measure of discrepancy is then defined between these estimates and the resulting dissimilarity matrix is used to carry out the required cluster analysis. Applications of this method to both simulated and real life data sets are discussed.

Principal components for multivariate functional data

A principal component method for multivariate functional data is proposed. Data can be arranged in a matrix whose elements are functions so that for each individual a vector of p functions is observed. This set of p curves is reduced to a small number of transformed functions, retaining as much information as possible. The criterion to measure the information loss is the integrated variance. Under mild regular conditions, it is proved that if the original functions are smooth this property is inherited by the principal components. A numerical procedure to obtain the smooth principal components is proposed and the goodness of the dimension reduction is assessed by two new measures of the proportion of explained variability. The method performs as expected in various controlled simulated data sets and provides interesting conclusions when it is applied to real data sets.

Reverse phase protein microarrays quantify and validate the bioenergetic signature as biomarker in colorectal cancer

A reverse phase protein microarray approach has been applied to quantify proteins of energy metabolism in normal and tumor biopsies of colorectal cancer (CRC) patients. The metabolic proteome of CRC specimens revealed a profound shift towards and enhanced glycolytic phenotype and concurrent mitochondrial alteration. The metabolic signature discriminated CRC patients with highly significant differences in overall and disease-free prognosis. The quantification of the bioenergetic signature of the tumor offers a relevant biomarker of CRC that could contribute in the handling of these patients.

Tests for the Second Order Stochastic Dominance Based on L -Statistics

We use some characterizations of convex and concave-type orders to define discrepancy measures useful in two testing problems involving stochastic dominance assumptions. The results are connected with the mean value of the order statistics and have a clear economic interpretation in terms of the expected cumulative resources of the poorest (or richest) in random samples. Our approach mainly consists of comparing the estimated means in ordered samples of the involved populations. The test statistics we derive are functions of L-statistics and are generated through estimators of the mean order statistics. We illustrate some properties of the procedures with simulation studies and an empirical example.

On the maximum bias functions of mm-estimates and constrained m-estimates of regression

We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the T-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is, the resulting CM-estimate dominates the S-estimate in terms of maxbias and, at the same time, is considerably more efficient.

A multivariate uniformity test for the case of unknown support

A test for the hypothesis of uniformity on a support S⊂ℝd is proposed. It is based on the use of multivariate spacings as those studied in Janson (Ann. Probab. 15:274–280, 1987). As a novel aspect, this test can be adapted to the case that the support S is unknown, provided that it fulfils the shape condition of λ-convexity. The consistency properties of this test are analyzed and its performance is checked through a small simulation study. The numerical problems involved in the practical calculation of the maximal spacing (which is required to obtain the test statistic) are also discussed in some detail.

The mRMR variable selection method: a comparative study for functional data

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the ‘most representative’ or ‘most relevant’ variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The minimum Redundance Maximum Relevance (mRMR) procedure, proposed by Ding and Peng [Minimum redundancy feature selection from microarray gene expression data. J Bioinform Comput Biol. 2005;3:185–205] and Peng et al. [Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy. IEEE Trans Pattern Anal Mach Intell. 2005;27:1226–1238] is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-called mutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Székely et al. [Measuring and testing dependence by correlation of distances. Ann Statist. 2007;35:2769–2794]. We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models sample sizes classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favour of the new proposed alternative.

A geometrically motivated parametric model in manifold estimation

The general aim of manifold estimation is reconstructing, by statistical methods, an m-dimensional compact manifold S on d (with m≤d) or estimating some relevant quantities related to the geometric properties of S. Focussing on the cases d=2 and d=3, with m=d or m=d−1, we will assume that the data are given by the distances to S from points randomly chosen on a band surrounding S. The aim of this paper is to show that, if S belongs to a wide class of compact sets (which we call sets with polynomial volume), the proposed statistical model leads to a relatively simple parametric formulation. In this setup, standard methodologies (method of moments, maximum likelihood) can be used to estimate some interesting geometric parameters, including curvatures and Euler characteristic. We will particularly focus on the estimation of the (d−1)-dimensional boundary measure (in Minkowskis sense) of S. It turns out, however, that the estimation problem is not straightforward since the standard estimators show a remarkably pathological behaviour: while they are consistent and asymptotically normal, their expectations are infinite. The theoretical and practical consequences of this fact are discussed in some detail.

Global robustness of location and dispersion estimates

We analyze the global robustness of location and dispersion estimates using the concept of relative explosion rate. The merits of several dispersion estimates are compared when the dispersion parameter itself is of main interest and also when they are auxiliary estimates needed to define scale equivariant location M-estimates. We have also compared location M-estimates and found that the choice of score function (its shape) is of secondary importance in comparison with the choice of the tuning constant and the auxiliary dispersion estimate. Finally, we use the explosion rate to assess the combined effect of the tuning constant and auxiliary dispersion estimate on the global robustness properties of location M-estimates.

Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order

A new methodology to detect zero-inflation and overdispersion is proposed, based on a comparison of the expected sample extremes among convexly ordered distributions. The method is very flexible and includes tests for the proportion of structural zeros in zero-inflated models, tests to distinguish between two ordered parametric families and a new general test to detect overdispersion. The performance of the proposed tests is evaluated via some simulation studies. For the well-known fetal lamb data, the conclusion is that the zero-inflated Poisson model should be rejected against other more disperse models, but the negative binomial model cannot be rejected.