McGill Statistics Seminar

Date: 2011-10-28

Time: 15:00-16:00

Location: BURN 1205

Abstract:

This paper considers the estimation of the parameters of a copula via a simulated method of moments type approach. This approach is attractive when the likelihood of the copula model is not known in closed form, or when the researcher has a set of dependence measures or other functionals of the copula, such as pricing errors, that are of particular interest. The proposed approach naturally also nests method of moments and generalized method of moments estimators. Combining existing results on simulation based estimation with recent results from empirical copula process theory, we show the consistency and asymptotic normality of the proposed estimator, and obtain a simple test of over-identifying restrictions as a goodness-of-fit test. The results apply to both iid and time series data. We analyze the finite-sample behavior of these estimators in an extensive simulation study. We apply the model to a group of seven financial stock returns and find evidence of statistically significant tail dependence, and that the dependence between these assets is stronger in crashes than booms.

Date: 2011-10-21

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Genome-wide association studies (GWAS) are used to identify physical positions (loci) on the genome where genetic variation is causally associated with a phenotype of interest at the population level. Typical studies are based on the measurement of several hundred thousand single nucleotide polymorphism (SNP) variants spread across the genome, in a few thousand individuals. The resulting datasets are large and require computationally efficient methods of statistical analysis.

Date: 2011-10-07

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, the following topics will be discussed: A class of bivariate probability integral transforms and Kendall distribution; bivariate quantile curves, central and lateral regions; non-exchangeability and radial asymmetry identification; new measures of nonexchangeability and radial asymmetry; financial applications and a few open problems (joint work with Flavio Ferreira).

Speaker

Nikolai Kolev is a Professor of Statistics at the University of Sao Paulo, Brazil.

Date: 2011-09-30

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Streaming data is ubiquitous in a wide range of areas from engineering and information technology, finance, and commerce, to atmospheric physics, and earth sciences. The online approximation of properties of data streams is of great interest, but this approximation process is hindered by the sheer size of the data and the speed at which it is generated. Data stream algorithms typically allow only one pass over the data, and maintain sub-linear representations of the data from which target properties can be inferred with high efficiency.

Date: 2011-09-23

Time: 15:30-16:30

Location: BURN 1205

Abstract:

In this talk, we give a basic introduction to Sumio Watanabe’s Singular Learning Theory, as outlined in his book “Algebraic Geometry and Statistical Learning Theory”. Watanabe’s key insight to studying singular models was to use a deep result in algebraic geometry known as Hironaka’s Resolution of Singularities. This result allows him to reparametrize the model in a normal form so that central limit theorems can be applied. In the second half of the talk, we discuss new algebraic methods where we define fiber ideals for discrete/Gaussian models. We show that the key to understanding the singular model lies in monomializing its fiber ideal.

Date: 2011-09-16

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Pair-copula constructions (PCCs) provide an elegant way to construct highly flexible multivariate distributions. However, for convenience of inference, pair-copulas are often assumed to depend on the conditioning variables only indirectly. In this talk, I will show how nonparametric smoothing techniques can be used to avoid this assumption. Model selection for PCCs will also be addressed within the proposed method.

Speaker

Elif F. Acar is a Postdoctoral Fellow in the Department of Mathematics and Statistics at McGill University. She holds a Ph.D. in Statistics from the University of Toronto.

Date: 2011-08-31

Time: 15:30-16:30

Location: BURN 1205

Abstract:

Volume estimators based on Cavalieri’s principle are widely used in the bio- sciences. For example in neuroscience, where volumetric measurements of brain structures are of interest, systematic samples of serial sections are obtained by magnetic resonance imaging or by a physical cutting procedure. The volume v is then estimated by ˆv, which is the sum over the areas of the structure of interest in the section planes multiplied by the width of the sections, t > 0. Assessing the precision of such volume estimates is a question of great practical importance, but statistically a challenging task due to the strong spatial dependence of the data and typically small sample sizes. In this talk, an overview of classical and new approaches to this problem will be presented. A special focus will be given to some recent advances on distribution estimators and confidence intervals for ˆv; see Hall and Ziegel (2011).