Amparo Baíllo

Local linear regression for functional predictor and scalar response

The aim of this work is to introduce a new nonparametric regression technique in the context of functional covariate and scalar response. We propose a local linear regression estimator and study its asymptotic behaviour. Its finite-sample performance is compared with a Nadayara-Watson type kernel regression estimator and with the linear regression estimator via a Monte Carlo study and the analysis of two real data sets. In all the scenarios considered, the local linear regression estimator performs better than the kernel one, in the sense that the mean squared prediction error is lower.

Convergence rates in nonparametric estimation of level sets

A level set of type {f[less-than-or-equals, slant]c} (where f is a density on and c is a positive value) can be estimated by its empirical version , where denotes a nonparametric (kernel) density estimator. We analyze, from two different points of view, the asymptotic behavior of the probability content of . Our results are motivated by applications in cluster analysis and outlier detection. Although the mathematical treatment is quite different in both cases, the conclusions are basically coincident. Roughly speaking, we show that the convergence rates are at most of type n-1/(d+2). For the univariate case d=1 this would be in the same spirit of the classical cube-root results found in some nonparametric setups.

EBI2 regulates CXCL13-mediated responses by heterodimerization with CXCR5

B‐cell movement into lymphoid follicles depends on the expression of the chemokine receptor CXCR5 and the recently reported Epstein‐Barr virus‐induced receptor 2 (EBI2). In cooperation with CXCR5, EBI2 helps to position activated B cells in the follicle, although the mechanism is poorly understood. Using human HEK293T cells and fluorescence resonance energy transfer (FRET) techniques, we demonstrate that CXCR5 and EBI2 form homo‐ and heterodimers. EBI2 expression modulated CXCR5 homodimeric complexes, as indicated by the FRET50 value (CXCR5 homodimer, 0.9851±0.0784; CXCR5 homodimer+EBI2, 1.7320±0.4905; P<0.05). HEK293T cells expressing CXCR5/EBI2 and primary activated murine B cells both down‐modulated CXCR5‐mediated responses, such as Ca2+ flux, cell migration, and MAPK activation; this modulation did not occur when primary B cells were obtained from EBI2–/– mice. The mechanism involves a reduction in binding affinity of the ligand (CXCL13) for CXCR5 (KD: 5.05×10–8 M for CXCR5 alone vs. 1.49×10–7 M for CXCR5/EBI2) and in the efficacy (Emax) of G‐protein activation in CXCR5/EBI2‐coexpressing cells (42.33±4.3%; P<0.05). These findings identify CXCR5/EBI2 heterodimers as functional units that contribute to the plasticity of CXCL13‐mediated B‐cell responses.—Barroso, R., Muñoz, L. Martínez., Barrondo, S., Vega, B., Holgado, B. L., Lucas, P., Baíllo, A., Sallés, J., Rodríguez‐Frade J. M., Mellado, M. EBI2 regulates CXCL13‐mediated responses by heterodimerization with CXCR5. FASEB J. 26, 4841–4854 (2012). www.fasebj.org

On the estimation of a star-shaped set

The estimation of a star-shaped set S from a random sample of points X 1,…,X n ∊ S is considered. We show that S can be consistently approximated (with respect to both the Hausdorff metric and the ‘distance in measure’ between sets) by an estimator ŝ n defined as a union of balls centered at the sample points with a common radius which can be chosen in such a way that ŝ n is also star-shaped. We also prove that, under some mild conditions, the topological boundary of the estimator ŝ n converges, in the Hausdorff sense, to that of S; this has a particular interest when the proposed estimation problem is considered from the point of view of statistical image analysis.

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.

Mean Squared Errors of Small Area Estimators under a Unit-Level Multivariate Model

This work deals with estimating the vector of means of certain characteristics of small areas. In this context, a unit level multivariate model with correlated sampling errors is considered. An approximation is obtained for the mean-squared and cross-product errors of the empirical best linear unbiased predictors of the means, when model parameters are estimated either by maximum likelihood (ML) or by restricted ML. This approach has been implemented on a Monte Carlo study using social and labour data from the Spanish Labour Force Survey.

A note on functional linear regression

This work focuses on the linear regression model with functional covariate and scalar response. We compare the performance of two (parametric) linear regression estimators and a nonparametric (kernel) estimator via a Monte Carlo simulation study and the analysis of two real data sets. The first linear estimator expands the predictor and the regression weight function in terms of the trigonometric basis, while the second one uses functional principal components. The choice of the regularization degree in the linear estimators is addressed.

Image estimators based on marked bins

The problem of approximating an ‘image’ S⊂ℝ d from a random sample of points is considered. If S is included in a grid of square bins, a plausible estimator of S is defined as the union of the ‘marked’ bins (those containing a sample point). We obtain convergence rates for this estimator and study its performance in the approximation of the border of S. The practical aspects of implementation are discussed, including some technical improvements on the estimator, whose performance is checked through a real data example.

A Test for Convex Dominance With Respect to the Exponential Class Based on an

We consider the problem of testing if a non-negative random variable is dominated, in the convex order, by the exponential class. Under the null hypothesis, the variable is harmonic new better than used in expectation (HNBUE), a well-known class of ageing distributions in reliability theory. As a test statistic, we propose the L1 norm of a suitable distance between the empirical and the exponential distributions, and we completely determine its asymptotic properties. The practical performance of our proposal is illustrated with simulation studies, which show that the asymptotic test has a good behavior and power, even for small sample sizes. Finally, three real data sets are analyzed.

L^1

Resonance energy transfer methods are in wide use for evaluating protein-protein interactions and protein conformational changes in living cells. Fluorescence resonance energy transfer (FRET) measures energy transfer as a function of the acceptor:donor ratio, generating FRET saturation curves. Modeling these curves by Michaelis-Menten kinetics allows characterization by two parameters, which serve to evaluate apparent affinity between two proteins and to compare this affinity in different experimental conditions. To reduce the effect of sampling variability, several statistical samples of the saturation curve are generated in the same biological conditions. Here we study three procedures to determine whether statistical samples in a collection are homogeneous, in the sense that they are extracted from the same regression model. From the hypothesis testing viewpoint, we considered an F test and a procedure based on bootstrap resampling. The third method analyzed the problem from the model selection viewpoint, and used the Akaike information criterion (AIC). Although we only considered the Michaelis-Menten model, all statistical procedures would be applicable to any other nonlinear regression model. We compared the performance of the homogeneity testing methods in a Monte Carlo study and through analysis in living cells of FRET saturation curves for dimeric complexes of CXCR4, a seven-transmembrane receptor of the G protein-coupled receptor family. We show that the F test, the bootstrap procedure and the model selection method lead in general to similar conclusions, although AIC gave the best results when sample sizes were small, whereas the F test and the bootstrap method were more appropriate for large samples. In practice, all three methods are easy to use simultaneously and show consistency, facilitating conclusions on sample homogeneity.