On central tendency and dispersion measures for intervals and hypercubes

The uncertainty or the variability of the data may be treated by considering, rather than a single value for each data, the interval of values in which it may fall. This paper studies the derivation of basic description statistics for interval-valued datasets. We propose a geometrical approach in the determination of summary statistics (central tendency and dispersion measures) for interval-valued variables

ClustOfVar: An R Package for the Clustering of Variables

Clustering of variables is as a way to arrange variables into homogeneous clusters, i.e., groups of variables which are strongly related to each other and thus bring the same information. These approaches can then be useful for dimension reduction and variable selection. Several specific methods have been developed for the clustering of numerical variables. However concerning qualitative variables or mixtures of quantitative and qualitative variables, far fewer methods have been proposed. The R package ClustOfVar was specifically developed for this purpose. The homogeneity criterion of a cluster is defined as the sum of correlation ratios (for qualitative variables) and squared correlations (for quantitative variables) to a synthetic quantitative variable, summarizing "as good as possible" the variables in the cluster. This synthetic variable is the first principal component obtained with the PCAMIX method. Two algorithms for the clustering of variables are proposed: iterative relocation algorithm and ascendant hierarchical clustering. We also propose a bootstrap approach in order to determine suitable numbers of clusters. We illustrate the methodologies and the associated package on small datasets

Les effets de l'adoption obligatoire des normes IFRS sur les incorporels : le cas de la France.

Cet article examine les effets de l'adoption obligatoire des IFRS sur les incorporels, dans le contexte français. Utilisant un échantillon de 83 entreprises issues du SBF 120, nous recherchons une typologie des pratiques comptables liées aux incorporels à la période de transition aux IFRS. Les résultats font ressortir trois classes d'entreprises affectées différemment par le passage aux normes internationales. La première classe est caractérisée par un changement important avec une forte augmentation du goodwill liée au retraitement d'immobilisations incorporelles comme les parts de marché. Elle permet d'illustrer la spécificité de la réglementation française. La deuxième classe se caractérise par une stabilité s'expliquant par le poids prédominant du goodwill sous référentiel français. Enfin la troisième classe ne subit pas non plus de changement compte tenu de la présence de marques en normes françaises. Le phénomène d'inertie décrit par Nobes (2006) selon lequel les traitements comptables pré-IFRS pourraient perdurer sous IFRS est vérifié.Analyse typologique, Goodwill, Incorporels, IFRS, transition.

Nonparametric instrumental regression with non-convex constraints

This paper considers the nonparametric regression model with an additive error that is dependent on the explanatory variables. As is common in empirical studies in epidemiology and economics, it also supposes that valid instrumental variables are observed. A classical example in microeconomics considers the consumer demand function as a function of the price of goods and the income, both variables often considered as endogenous. In this framework, the economic theory also imposes shape restrictions on the demand function, like integrability conditions. Motivated by this illustration in microeconomics, we study an estimator of a nonparametric constrained regression function using instrumental variables by means of Tikhonov regularization. We derive rates of convergence for the regularized model both in a deterministic and stochastic setting under the assumption that the true regression function satisfies a projected source condition including, because of the non-convexity of the imposed constraints, an additional smallness condition

Discretization of variational regularization in Banach spaces

Consider a nonlinear ill-posed operator equation $F(u)=y$ where $F$ is defined on a Banach space $X$. In general, for solving this equation numerically, a finite dimensional approximation of $X$ and an approximation of $F$ are required. Moreover, in general the given data \yd of $y$ are noisy. In this paper we analyze finite dimensional variational regularization, which takes into account operator approximations and noisy data: We show (semi-)convergence of the regularized solution of the finite dimensional problems and establish convergence rates in terms of Bregman distances under appropriate sourcewise representation of a solution of the equation. The more involved case of regularization in nonseparable Banach spaces is discussed in detail. In particular we consider the space of finite total variation functions, the space of functions of finite bounded deformation, and the $L^\infty$--space

Structural Basis of Teneurin-Latrophilin Interaction in Repulsive Guidance of Migrating Neurons

Teneurins are ancient metazoan cell adhesion receptors that control brain development and neuronal wiring in higher animals. The extracellular C terminus binds the adhesion GPCR Latrophilin, forming a trans-cellular complex with synaptogenic functions. However, Teneurins, Latrophilins, and FLRT proteins are also expressed during murine cortical cell migration at earlier developmental stages. Here, we present crystal structures of Teneurin-Latrophilin complexes that reveal how the lectin and olfactomedin domains of Latrophilin bind across a spiraling beta-barrel domain of Teneurin, the YD shell. We couple structure-based protein engineering to biophysical analysis, cell migration assays, and in utero electroporation experiments to probe the importance of the interaction in cortical neuron migration. We show that binding of Latrophilins to Teneurins and FLRTs directs the migration of neurons using a contact repulsion-dependent mechanism. The effect is observed with cell bodies and small neurites rather than their processes. The results exemplify how a structure-encoded synaptogenic protein complex is also used for repulsive cell guidance

The Iteratively Regularized Gau{\ss}-Newton Method with Convex Constraints and Applications in 4Pi-Microscopy

This paper is concerned with the numerical solution of nonlinear ill-posed operator equations involving convex constraints. We study a Newton-type method which consists in applying linear Tikhonov regularization with convex constraints to the Newton equations in each iteration step. Convergence of this iterative regularization method is analyzed if both the operator and the right hand side are given with errors and all error levels tend to zero. Our study has been motivated by the joint estimation of object and phase in 4Pi microscopy, which leads to a semi-blind deconvolution problem with nonnegativity constraints. The performance of the proposed algorithm is illustrated both for simulated and for three-dimensional experimental data

Orthogonal rotation in PCAMIX

Kiers (1991) considered the orthogonal rotation in PCAMIX, a principal component method for a mixture of qualitative and quantitative variables. PCAMIX includes the ordinary principal component analysis (PCA) and multiple correspondence analysis (MCA) as special cases. In this paper, we give a new presentation of PCAMIX where the principal components and the squared loadings are obtained from a Singular Value Decomposition. The loadings of the quantitative variables and the principal coordinates of the categories of the qualitative variables are also obtained directly. In this context, we propose a computationaly efficient procedure for varimax rotation in PCAMIX and a direct solution for the optimal angle of rotation. A simulation study shows the good computational behavior of the proposed algorithm. An application on a real data set illustrates the interest of using rotation in MCA. All source codes are available in the R package "PCAmixdata"