/categories/mcgill-statistics-seminar/index.xml McGill Statistics Seminar - McGill Statistics Seminars

McGill Statistics Seminar

  • A Bayesian finite mixture of bivariate regressions model for causal mediation analyses

    Geneviève Lefebvre · Oct 14, 2016

    Date: 2016-10-14

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Building on the work of Schwartz, Gelfand and Miranda (Statistics in Medicine (2010); 29(16), 1710-23), we propose a Bayesian finite mixture of bivariate regressions model for causal mediation analyses. Using an identifiability condition within each component of the mixture, we express the natural direct and indirect effects of the exposure on the outcome as functions of the component-specific regression coefficients. On the basis of simulated data, we examine the behaviour of the model for estimating these effects in situations where the associations between exposure, mediator and outcome are confounded, or not. Additionally, we demonstrate that this mixture model can be used to account for heterogeneity arising through unmeasured binary mediator-outcome confounders. Finally, we apply our mediation mixture model to estimate the natural direct and indirect effects of exposure to inhaled corticosteroids during pregnancy on birthweight using a cohort of asthmatic women from the province of Québec.

  • Cellular tree classifiers

    Luc Devroye · Oct 7, 2016

    Date: 2016-10-07

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Suppose that binary classification is done by a tree method in which the leaves of a tree correspond to a partition of d-space. Within a partition, a majority vote is used. Suppose furthermore that this tree must be constructed recursively by implementing just two functions, so that the construction can be carried out in parallel by using “cells”: first of all, given input data, a cell must decide whether it will become a leaf or internal node in the tree. Secondly, if it decides on an internal node, it must decide how to partition the space linearly. Data are then split into two parts and sent downstream to two new independent cells. We discuss the design and properties of such classifiers.

  • CoCoLasso for high-dimensional error-in-variables regression

    Hui Zou · Sep 30, 2016

    Date: 2016-09-30

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright (2012) proposed a non-convex modification of the Lasso for doing high-dimensional regression with noisy and missing data. It is generally agreed that the virtues of convexity contribute fundamentally the success and popularity of the Lasso. In light of this, we propose a new method named CoCoLasso that is convex and can handle a general class of corrupted datasets including the cases of additive measurement error and random missing data. We establish the estimation error bounds of CoCoLasso and its asymptotic sign-consistent selection property. We further elucidate how the standard cross validation techniques can be misleading in presence of measurement error and develop a novel corrected cross-validation technique by using the basic idea in CoCoLasso. The corrected cross-validation has its own importance. We demonstrate the superior performance of our method over the non-convex approach by simulation studies.

  • Stein estimation of the intensity parameter of a stationary spatial Poisson point process

    Jean-François Coeurjolly · Sep 23, 2016

    Date: 2016-09-23

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We revisit the problem of estimating the intensity parameter of a homogeneous Poisson point process observed in a bounded window of $R^d$ making use of a (now) old idea going back to James and Stein. For this, we prove an integration by parts formula for functionals defined on the Poisson space. This formula extends the one obtained by Privault and Réveillac (Statistical inference for Stochastic Processes, 2009) in the one-dimensional case and is well-suited to a notion of derivative of Poisson functionals which satisfy the chain rule. The new estimators can be viewed as biased versions of the MLE with a tailored-made bias designed to reduce the variance of the MLE. We study a large class of examples and show that with a controlled probability the corresponding estimator outperforms the MLE. We illustrate in a simulation study that for very reasonable practical cases (like an intensity of 10 or 20 of a Poisson point process observed in the d-dimensional euclidean ball of with d = 1, …, 5), we can obtain a relative (mean squared error) gain above 20% for the Stein estimator with respect to the maximum likelihood. This is a joint work with M. Clausel and J. Lelong (Univ. Grenoble Alpes, France).

  • Two-set canonical variate model in multiple populations with invariant loadings

    Fei Gu · Sep 9, 2016

    Date: 2016-09-09

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    Goria and Flury (Definition 2.1, 1996) proposed the two-set canonical variate model (referred to as the CV-2 model hereafter) and its extension in multiple populations with invariant weight coefficients (Definition 2.2). The equality constraints imposed on the weight coefficients are in line with the approach to interpreting the canonical variates (i.e., the linear combinations of original variables) advocated by Harris (1975, 1989), Rencher (1988, 1992), and Rencher and Christensen (2003). However, the literature in psychology and education shows that the standard approach adopted by most researchers, including Anderson (2003), is to use the canonical loadings (i.e., the correlations between the canonical variates and the original variables in the same set) to interpret the canonical variates. In case of multicollinearity (giving rise to the so-called suppression effects) among the original variables, it is not uncommon to obtain different interpretations from the two approaches. Therefore, following the standard approach in practice, an alternative (probably more realistic) extension of Goria and Flury’s CV-2 model in multiple populations is to impose the equality constraints on the canonical loadings. The utility of this multiple-population extension are illustrated with two numeric examples.

  • Multivariate tests of associations based on univariate tests

    Ruth Heller · Apr 8, 2016

    Date: 2016-04-08

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    For testing two random vectors for independence, we consider testing whether the distance of one vector from an arbitrary center point is independent from the distance of the other vector from an arbitrary center point by a univariate test. We provide conditions under which it is enough to have a consistent univariate test of independence on the distances to guarantee that the power to detect dependence between the random vectors increases to one, as the sample size increases. These conditions turn out to be minimal. If the univariate test is distribution-free, the multivariate test will also be distribution-free. If we consider multiple center points and aggregate the center-specific univariate tests, the power may be further improved. We suggest a specific aggregation method for which the resulting multivariate test will be distribution-free if the univariate test is distribution-free. We show that several multivariate tests recently proposed in the literature can be viewed as instances of this general approach.

  • Asymptotic behavior of binned kernel density estimators for locally non-stationary random fields

    Michel Harel · Apr 1, 2016

    Date: 2016-04-01

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In this talk, I will describe the finite- and large-sample behavior of binned kernel density estimators for dependent and locally non-stationary random fields converging to stationary random fields. In addition to looking at the bias and asymptotic normality of the estimators, I will present results from a simulation study which shows that the kernel density estimator and the binned kernel density estimator have the same behavior and both estimate accurately the true density when the number of fields increases. This work finds applications in various fields, including the study of epidemics and mining research. My specific illustration will be concerned with the 2002 incidence rates of tuberculosis in the departments of France.

  • Robust minimax shrinkage estimation of location vectors under concave loss

    William E. Strawderman · Mar 18, 2016

    Date: 2016-03-18

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We consider the problem of estimating the mean vector, q, of a multivariate spherically symmetric distribution under a loss function which is a concave function of squared error. In particular we find conditions on the shrinkage factor under which Stein-type shrinkage estimators dominate the usual minimax best equivariant estimator. In problems where the scale is known, minimax shrinkage factors which generally depend on both the loss and the sampling distribution are found. When the scale is estimated through the squared norm of a residual vector, for a large subclass of concave losses, we find minimax shrinkage factors which are independent of both the loss and the underlying distribution. Recent applications in predictive density estimation are examples where such losses arise naturally.

  • Nonparametric graphical models: Foundation and trends

    Han Liu · Mar 11, 2016

    Date: 2016-03-11

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    We consider the problem of learning the structure of a non-Gaussian graphical model. We introduce two strategies for constructing tractable nonparametric graphical model families. One approach is through semiparametric extension of the Gaussian or exponential family graphical models that allows arbitrary graphs. Another approach is to restrict the family of allowed graphs to be acyclic, enabling the use of fully nonparametric density estimation in high dimensions. These two approaches can both be viewed as adding structural regularization to a general pairwise nonparametric Markov random field and reflect an interesting tradeoff of model flexibility with structural complexity. In terms of graph estimation, these methods achieve the optimal parametric rates of convergence. In terms of computation, these methods are as scalable as the best implemented parametric methods. Such a “free-lunch phenomenon” makes them extremely attractive for large-scale applications. We will also introduce several new research directions along this line of work, including latent-variable extension, model-based nonconvex optimization, graph uncertainty assessment, and nonparametric graph property testing.

  • Aggregation methods for portfolios of dependent risks with Archimedean copulas

    Etienne Marceau · Feb 26, 2016

    Date: 2016-02-26

    Time: 15:30-16:30

    Location: BURN 1205

    Abstract:

    In this talk, we will consider a portfolio of dependent risks represented by a vector of dependent random variables whose joint cumulative distribution function (CDF) is defined with an Archimedean copula. Archimedean copulas are very popular and their extensions, nested Archimedean copulas, are well suited for vectors of random vectors in high dimension. I will describe a simple approach which makes it possible to compute the CDF of the sum or a variety of other functions of those random variables. In particular, I will derive the CDF and the TVaR of the sum of those risks using the Frank copula, the Shifted Negative Binomial copula, and the Ali-Mikhail-Haq (AMH) copula. The computation of the contribution of each risk under the TVaR-based allocation rule will also be illustrated. Finally, the links between the Clayton copula, the Shifted Negative Binomial copula, and the AMH copula will be discussed.