Contour regression: A general approach to dimension reduction

We propose a novel approach to sufficient dimension reduction in regression, based on estimating contour directions of small variation in the response. These directions span the orthogonal complement of the minimal space relevant for the regression and can be extracted according to two measures of variation in the response, leading to simple and general contour regression (SCR and GCR) methodology. In comparison with existing sufficient dimension reduction techniques, this contour-based methodology guarantees exhaustive estimation of the central subspace under ellipticity of the predictor distribution and mild additional assumptions, while maintaining \sqrtn-consistency and computational ease. Moreover, it proves robust to departures from ellipticity. We establish population properties for both SCR and GCR, and asymptotic properties for SCR. Simulations to compare performance with that of standard techniques such as ordinary least squares, sliced inverse regression, principal Hessian directions and sliced average variance estimation confirm the advantages anticipated by the theoretical analyses. We demonstrate the use of contour-based methods on a data set concerning soil evaporation.Comment: Published at http://dx.doi.org/10.1214/009053605000000192 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Reduction Paradigm for Multivariate Laws

A "reduction paradigm" is a theoretical framework which provides a definition of structures for multivariate laws, and allows to simplify their representation and statistical analysis. The main idea is to decompose a law as the superimposition of a "structural term" and a "noise," so that the latter can be neglected "without loss of information on the structure." When the lower structural term is supported by a lower-dimensional affine subspace, an "exhaustive dimension reduction" is achieved. We describe the reduction paradigm that results from selecting white noises, and convolution as superposition mechanism

On Multivariate Structures and Exhaustive Reductions

Simplified representations of multivariate laws, and in particular those allowing one to decrease the dimension while preserving structural information, are of paramount importance in statistical analysis. This paper concerns the "theoretical premises" of simplification. We introduce a framework that allows us to specify as "partitions" of probability laws on a Euclidian space, we show how they can be generated via "partial orders," or "binary operation" and "noise classes." Moreover, the framework allows us to identify "simplified representations" that are guaranteed to be "exhaustive" with respect to such definitions, and might live in "lower dimensions.

Composite likelihood inference in a discrete latent variable model for two-way "clustering-by-segmentation" problems

We consider a discrete latent variable model for two-way data arrays, which allows one to simultaneously produce clusters along one of the data dimensions (e.g. exchangeable observational units or features) and contiguous groups, or segments, along the other (e.g. consecutively ordered times or locations). The model relies on a hidden Markov structure but, given its complexity, cannot be estimated by full maximum likelihood. We therefore introduce composite likelihood methodology based on considering different subsets of the data. The proposed approach is illustrated by simulation, and with an application to genomic data

El entrenamiento reatribucional como intervención para la mejora del rendimiento académico

[Resumen] Se presenta una revisión sobre la función que desempeñan las atribuciones causales en el rendimiento académico. En primer lugar, se hace referencia a un ejemplo que muestra como la conducta y las emociones pueden cambiar al atribuir el mismo resultado a diferentes causas.- A continuación se describen las dimensiones principales en que pueden ser ordenadas las atribuciones causales.- De forma detallada se indican cuales son las consecuencias de los distintos tipos de explicaciones causales sobre la motivación, el estado emocional y la autoestima.- Por último, se hace mención de los estilos atribucionales que son adaptativos y desadaptativos para el rendimiento académico y la posibilidad de modificar estos últimos a través del feedback que proporciona el entrenamiento reatribucional

Modeling a Decentralized Asset Market: An Introduction the Financial "Toy Room"

In this paper, the authors describe a micro-founded simulation environment for decentralized trade in a financial asset. Within the philosophy of computer-simulated "artificial markets", this environment allows one to experiment in a modular fashion with (i) individual characterizations in terms of behaviors and learning, (ii) different architectural and institutional traits of the market, and (iii) time-embedding of events at the system and the individual level

Some Preliminary Experiments with the Financial "Toy-Room"

We describe some preliminary experiments realized with Financial "Toy-Room" (a micro-founded simulation environment for decentralized trade in a homogeneous financial asset). The experiments are aimed at testing the system, and exploring its flexibility in depicting specific contexts as sub-cases. For this purpose, we selected an issue that has been widely investigated in the literature: the existence and characterization of markets in which prices are (or are believed to be) "quality signals" passing information from informed to uninformed traders. In our out-of-equilibrium simulation analysis, we take agents to trade based on a "spread rule," and introduce "dis-synchronization" in agents' updating processes. Thus, we investigate how dis-synchronization, updating paces and spreads affect persistence of trade and the time-path of prices in extreme regimes (i.e. when all agents are informed, or all agents are uninformed)

Modeling a Decentralized Asset Market: An Introduction to the Financial "Toy-Room"

In this paper, we describe a micro-founded simulation enviroment for decentralized trade in financial asset. Within the philosophy of computer simulated "artificial markets", this enviroments allows one to experiment in a modular fashion with (i) individual characterizations in terms of behaviors and learning, (ii) different architectural and institutional traits of the market, and (iii) time-embedding of events at the system and the individual level.-