Partially linear models on Riemannian manifolds

In partially linear models the dependence of the response y on (x^T,t) is modeled through the relationship y=\x^T \beta+g(t)+\epsilon where \epsilon is independent of (x^T,t). In this paper, estimators of \beta and g are constructed when the explanatory variables t take values on a Riemannian manifold. Our proposal combine the flexibility of these models with the complex structure of a set of explanatory variables. We prove that the resulting estimator of \beta is asymptotically normal under the suitable conditions. Through a simulation study, we explored the performance of the estimators. Finally, we applied the studied model to an example based on real dataset.Comment: 7 pages, 2 figure

Empirical likelihood based testing for regression

Consider a random vector $(X,Y)$ and let $m(x)=E(Y|X=x)$. We are interested in testing $H_0:m\in {\cal M}_{\Theta,{\cal G}}=\{\gamma(\cdot,\theta,g):\theta \in \Theta,g\in {\cal G}\}$ for some known function $\gamma$, some compact set $\Theta \subset$IR$^p$ and some function set ${\cal G}$ of real valued functions. Specific examples of this general hypothesis include testing for a parametric regression model, a generalized linear model, a partial linear model, a single index model, but also the selection of explanatory variables can be considered as a special case of this hypothesis. To test this null hypothesis, we make use of the so-called marked empirical process introduced by \citeD and studied by \citeSt for the particular case of parametric regression, in combination with the modern technique of empirical likelihood theory in order to obtain a powerful testing procedure. The asymptotic validity of the proposed test is established, and its finite sample performance is compared with other existing tests by means of a simulation study.Comment: Published in at http://dx.doi.org/10.1214/07-EJS152 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

The bootstrap -A review

The bootstrap, extensively studied during the last decade, has become a powerful tool in different areas of Statistical Inference. In this work, we present the main ideas of bootstrap methodology in several contexts, citing the most relevant contributions and illustrating with examples and simulation studies some interesting aspects

Análisis multidisciplinar de la delincuencia socioeconómica

Traballo fin de grao (UDC.DER). Dereito. Curso 2012/201