Statistical Methods and Applications 1

Statistical Methods and Applications 1 
Chair: David Spiegelhalter (Cambridge University) 

JINGJIA CHU, University of Western Ontario
A Multivariate Time Series Model with an Additive GARCH Type Structure  [PDF]
A new class of multivariate time series model with an additive GARCH type structure was proposed, which could be used to capture the common risk among equities. The dynamic conditional covariances between series are aggregated by a common risk term, which has been the key to characterize the conditional correlation. The model ergodicity and stationarity were proved as well as the identifiability theorem in terms of the second moment. A Monte Carlo simulation example will be shown in the talk. 
REYHANEH HOSSEINI, University of Ottawa
A Bayesian Nonparametric Chi-squared Goodness-of-fit Test  [PDF]
The Bayesian nonparametric inference and Dirichlet process are popular tools in statistical methodologies. In this work, we employ the Dirichlet process in hypothesis testing to propose a Bayesian nonparametric chi-squared goodness-of-fit test. In our Bayesian nonparametric approach, we consider the Dirichlet process as the prior for the distribution of data and carry out the test based on the Kullback-Leibler distance between the updated Dirichlet process and the hypothesized distribution. We prove that this distance asymptotically converges to the same chi-squared distribution as the classical test does. Similarly, a Bayesian nonparametric chi-squared test of independence for a contingency table is provided. 
AURÉLIEN GUETSOP NANGUE, Université de Montréal
Approximations to Permutation Tests of Independence Between Two Random Vectors [PDF]
The main result establishes the equivalence of power between the α-distance covariance and the Hilbert-Schmidt independence criterion (HSIC) tests with the characteristic kernel of a stable probability distribution of index α with a sufficiently small bandwidth. Large-scale simulations reveal the superiority of these tests over other tests using copula. The Pearson type III approximation to the exact permutation distribution yields tests with more accurate type I error rates than the gamma approximation used for HSIC. A new method for bandwidth selection in HSIC tests is proposed which improves power in three simulations, two of which are from machine learning. 
AURÉLIEN NICOSIA, Université Laval
Equivalence Between the Random Walk Model in the Plane and Conditional Logistic Regression in a Multi-State Framework, with Application to the Analysis of Animal Movement  [PDF]
In this talk, we introduce a multi-state version of conditional logistic regression that compares the locations that an animal has chosen with randomly sampled locations. The impacts of different sampling procedures are discussed. A hidden process structure enables the modeling of situations where the animal exhibits various choice behaviors. We prove its equivalence with a random walk model in the plane, in which the directional part of the process is an angular regression model. We illustrate the use of the methods by modeling the movement of an animal in Prince Albert National Park (Saskatchewan, Canada). 
A Moment-Based Bivariate Density Estimation Methodology for Large Data Sets  [PDF]
We propose a moment-based methodology for approximating the density function associated with a bivariate distribution, which consists in applying an adjustment involving orthogonal polynomials to an initial density approximation. The use of standard polynomials is then shown to be mathematically equivalent. As well, the proposed technique is extended to the estimation of bivariate density functions, in which case joint sample moments are being utilized. It will be explained that this approach is ideally suited to model `big data', which will be illustrated by applying it to large data sets. Generalizations to multivariate distributions shall also be discussed. 
BANGXIN ZHAO, Western University
Distance Techniques for High-dimensional Influence Measure  [PDF]
In this talk, a new statistic based on Hellinger Distance is developed to evaluate the influence of individual observation on high-dimensional data. We first give the rigorous definition of this statistic which itself is a function of probability mass functions based on marginal correlations, and then explain how this statistic accurately evaluates the influence of individual observations. The asymptotic distribution of the proposed statistic can be found by setting the dimension of the explanatory variable to approach infinity, which shows inference can also be conducted. Simulation and real data analysis are given as illustration of the usefulness of the proposed method.