03/05/2013

Departamento de Estadística. Facultad de Matemáticas.
Seminario de Estadística
Inference on Financial Bubbles
Ricardo Bórquez
Pontificia Universidad Católica de Chile
Sala 1 - 12:00 Hrs. Facultad de Matemáticas

Abstract

Testing for rational bubbles in financial asset prices has proven to be difficult. A cite quote from Gürkaynak (J. Econ. Surveys, 2008) states: “For each paper that finds evidence of bubbles, there is another one that fits the data equally well without allowing for a bubble”. In the context of the simple stock price model it has been suggested that a rational bubble cannot be distinguished from the fundamental price. We show that this assertion is true not only for the stock price model but for any fundamental price that is determined by arbitrage arguments. In particular, bubbles defined as processes with explosive conditional mean -which is standard in the financial literature- are identified only on a set of null probability. More in general, because identification of rational bubbles is symmetric to the identification of the fundamental price, the latter requires the characterization of some identifying restrictions, which take the form of necessary transversality conditions (NTCs) for the respective price model. NTCs for the class of Markov and Harrison recurrent price processes are derived.

26/04/2013

Departamento de Estadística. Facultad de Matemáticas.
Seminario de Estadística
Functional area under the curve regression: a metabolic syndrome case study
Vanda Inácio de Carvalho
Pontificia Universidad Católica de Chile
Sala 1 - Facultad de Matemáticas - 12:00 Hrs.

Abstract
The statistical evaluation of diagnostic tests and screening procedures is of great importance in public health and medical research. New diagnostic and screening procedures must be rigorously evaluated in order to determine their abilities to discriminate between diseased and nondiseased states. Characterization of factors affecting test performance is a crucial step in the evaluation process. It is important to understand the covariate influence to determine the optimal and suboptimal populations to perform such tests on. We develop nonparametric regression methods for the area under the receiver operating characteristic curve, a well-accepted summary measure of diagnostic test accuracy, for the case  where the covariate influencing the test´s performance is functional. The corresponding estimator generalizes the two-sample Mann--Whitney statistic approach for comparing two populations by taking a functional covariate effect into account. The simulation study shows that the method produces estimates with small bias and small mean squared error. Application of the method to evaluate the influence of the nocturnal levels of arterial oxygen saturation of hemoglobin on the performance of the gamma-glutamyl-transferase to diagnosis women with metabolic syndrome reveals that this marker performs better in women with no respiratory problems

12/04/2013

Departamento de Estadística. Facultad de Matemáticas.
Semianrio de Estadística
Bayesian P-spline mixture modeling of extreme forest temperatures
Miguel de Carvalho
Pontificia Universidad Católica de Chile
Sala 1 - Facultad de Matemáticas - 12:00 Hrs

05/04/2013

Departamento de Estadística. Facultad de Matemáticas.
Seminarios de Estadística
Compactly supported correlation functions in multivariate Geostatistics
Emilio Porcu

Sala 1 - 12:00 Hrs. Facultad de Matemáticas _PUC

Abstract:
We propose a new family of matrix--valued covariance functions being compactly supported over balls of R^d with given radii. We show the mathematical construction and then illustrate the statistical features as well as the computational gains obtained for estimating the spatial dependence through maximum likelihood techniques.

05/04/2013

Departamento de Estadística. Facultad de Matemáticas.
Seminario de Estadística
Estimating covariance models in large spatio-temporal data: the covariance quasi tapering method
Moreno Bevilacqua

Sala 1 - 12:00 Facultad de Matemáticas

Abstract:
In the last years there has been a growing interest in proposing methods for estimating covariance functions for geostatistical spatio temporal data. Among these, maximum likelihood estimates have nice features when we deal with a Gaussian model. However maximum likelihood becomes impractical when the number of observations is very large in time or in space. We present the method of the covariance quasi tapering as an alternative of the maximum likelihood estimation and we describe the statistical and computational properties of the method.