2013 Winter

Date: 2013-04-12 Time: 14:30-15:30 Location: Concordia Abstract: Estimation of large dimensional covariance matrix has been of interest recently. One model assumes that there are $p$ dimensional independent identically distributed Gaussian observations $X_1, \ldots , X_n$ with dispersion matrix $\Sigma_p$ and $p$ grows much faster than $n$. Appropriate convergence rate results have been established in the literature for tapered and banded estimators of $\Sigma_p$ which are based on the sample variance covariance matrix of $n$ observations.

Date: 2013-04-05 Time: 14:30-15:30 Location: BURN 1205 Abstract: We consider the problem of predictive density estimation under Kullback-Leibler loss when the parameter space is restricted to a convex subset. The principal situation analyzed relates to the estimation of an unknown predictive p-variate normal density based on an observation generated by another p-variate normal density. The means of the densities are assumed to coincide, the covariance matrices are a known multiple of the identity matrix.

Date: 2013-03-22 Time: 14:30-15:30 Location: BURN 107 Abstract: We give a characterization of the hyper Dirichlet distribution hyper Markov with respect to a decomposable graph $G$ (or equivalently a moral directed acyclic graph). For $X=(X_1,\ldots,X_d)$ following the hyper Dirichlet distribution, our characterization is through the so-called “local and global independence properties” for a carefully designed family of orders of the variables $X_1,\ldots,X_d$. The hyper Dirichlet for general directed acyclic graphs was derived from a characterization of the Dirichlet distribution given by Geiger and Heckerman (1997).

Date: 2013-03-15 Time: 14:30-15:30 Location: BURN 1205 Abstract: Join work with Yukun Liu (East China Normal University) Population quantiles and their functions are important parameters in many applications. For example, the lower level quantiles often serve as crucial quality indices of forestry products and others. In the presence of several independent samples from populations satisfying density ratio model, we investigate the properties of the empirical likelihood (EL) based inferences of quantiles and their functions.

Date: 2013-03-01 Time: 14:30-15:30 Location: BURN 1205 Abstract: Some problems of statistics can be reduced to extremal problems of minimizing functionals of smooth functions defined on the cube $[0,1]^m$, $m\geq 2$. In this talk, we consider a class of extremal problems that is closely connected to the problem of testing multivariate independence. By solving the extremal problem, we provide a unified approach to establishing weak convergence for a wide class of empirical processes which emerge in connection with testing multivariate independence.

Date: 2013-02-22 Time: 14:30-15:30 Location: CRM, Université de Montréal, Pav. André-Ainsenstadt, salle 1360 Abstract: In this talk, we first provide an overview of issues arising from and methods dealing with complex survey data in the presence of missing observations, with a major focus on the estimating equation approach for analysis and imputation methods for missing data. We then propose a semiparametric fractional imputation method for handling item nonresponses, assuming certain baseline auxiliary variables can be observed for all units in the sample.

Date: 2013-02-15 Time: 14:30-15:30 Location: BURN 1205 Abstract: It is often crucial to know whether the dependence structure of a bivariate distribution belongs to the class of extreme-­‐value copulas. In this talk, I will describe a graphical tool that allows judgment regarding the existence of extreme-­‐value dependence. I will also present a data-­‐ driven nonparametric estimator of the Pickands dependence function. This estimator, which is constructed from constrained b-­‐splines, is intrinsic and differentiable, thereby enabling sampling from the fitted model.

Date: 2013-02-08 Time: 14:30-15:30 Location: BURN 1205 Abstract: In the context of univariate association tests between a trait of interest and common genetic variants (SNPs) across the whole genome, corrections for multiple testing have been well-studied. Due to the patterns of correlation (i.e. linkage disequilibrium), the number of independent tests remains close to 1 million, even when many more common genetic markers are available. With the advent of the DNA sequencing era, however, newly-identified genetic variants tend to be rare or even unique, and consequently single-variant tests of association have little power.

Date: 2013-02-01 Time: 14:30-15:30 Location: BURN 1205 Abstract: I will consider the task of estimating high-dimensional Gaussian graphical models (or networks) corresponding to a single set of features under several distinct conditions. In other words, I wish to estimate several distinct but related networks. I assume that most aspects of the networks are shared, but that there are some structured differences between them. The goal is to exploit the similarity among the networks in order to obtain more accurate estimates of each individual network, as well as to identify the differences between the networks.

Date: 2013-01-25 Time: 14:30-15:30 Location: BURN 1205 Abstract: In an attempt to improve on the Metropolis algorithm, various MCMC methods with auxiliary variables, such as the multiple-try and delayed rejection Metropolis algorithms, have been proposed. These methods generate several candidates in a single iteration; accordingly they are computationally more intensive than the Metropolis algorithm. It is usually difficult to provide a general estimate for the computational cost of a method without being overly conservative; potentially efficient methods could thus be overlooked by relying on such estimates.