An embedding result

In unbounded subset $\Omega$ in $R^n$ we study the operator $u\rightarrow gu$ as an operator defined in the Sobolev space $W^{r,p}(\Omega)$ and which takes values in $L^p(\Omega)$. The functions $g$ belong to wider spaces of $L^p$ connected with the Morrey type spaces. The main result is an embedding theorem from which we can deduce a Fefferman type inequality.Comment: 6 page

msBP: An R package to perform Bayesian nonparametric inference using multiscale Bernstein polynomials mixtures

msBP is an R package that implements a new method to perform Bayesian multiscale nonparametric inference introduced by Canale and Dunson (2016). The method, based on mixtures of multiscale beta dictionary densities, overcomes the drawbacks of Pólya trees and inherits many of the advantages of Dirichlet process mixture models. The key idea is that an infinitely-deep binary tree is introduced, with a beta dictionary density assigned to each node of the tree. Using a multiscale stick-breaking characterization, stochastically decreasing weights are assigned to each node. The result is an infinite mixture model. The package msBP implements a series of basic functions to deal with this family of priors such as random densities and numbers generation, creation and manipulation of binary tree objects, and generic functions to plot and print the results. In addition, it implements the Gibbs samplers for posterior computation to perform multiscale density estimation and multiscale testing of group differences described in Canale and Dunson (2016)

A Lower Bound for Chaos on the Elliptical Stadium

The elliptical stadium is a plane region bounded by a curve constructed by joining two half-ellipses by two parallel segments of equal length. The billiard inside it, as a map, generates a two parameters family of dynamical systems. It is known that the system is ergodic for a certain region of the parameter space. In this work we study the stability of a particular family of periodic orbits obtaining good bounds for the chaotic zone.Comment: 13 pages, LaTeX. 7 postscript low resolution figures included. High resolution figures avaiable under request to [email protected]

Efficiency and News in Exchange Rate Market. The Euro/Dollar Case

The aim of the paper is twofold: the first one is to examine the theoretical points that constitute literature on exchange rate market efficiency. We give a quick look to the long run, in which high or low efficiency results from the adjustment velocity of prices and production in goods market. We then go to examine literature conclusions about the short run. The second aim is to test the efficiency for the US dollar against the Euro foreign exchange market with a `news’ exchange rate model using daily data over a period of 19 months. In the model we use, as proxies of ‘news’, variables generated by the residuals from a VAR model. Our results are consistent with the hypothesis that the forward exchange rate is not an unbiased predictor of the future spot rate. That is, we reject the hypothesis of efficiency and we show the importance of the ‘news’ in determining short-run movements in the exchange rate markets. The general conclusion we reach is that the euro dollar exchange rate market, from its birth to august 2000, is not efficient because expectations could not be rational, i.e. operators cannot predict risks coming from stock exchange and from uncertainty on future values of economic variables

Nonparametric Bayes modeling of count processes

Data on count processes arise in a variety of applications, including longitudinal, spatial and imaging studies measuring count responses. The literature on statistical models for dependent count data is dominated by models built from hierarchical Poisson components. The Poisson assumption is not warranted in many applications, and hierarchical Poisson models make restrictive assumptions about over-dispersion in marginal distributions. This article proposes a class of nonparametric Bayes count process models, which are constructed through rounding real-valued underlying processes. The proposed class of models accommodates applications in which one observes separate count-valued functional data for each subject under study. Theoretical results on large support and posterior consistency are established, and computational algorithms are developed using Markov chain Monte Carlo. The methods are evaluated via simulation studies and illustrated through application to longitudinal tumor counts and asthma inhaler usage