2016-Statistical Methods and Applications 2


Statistical Methods and Applications 2 
Chair: William Aeberhard (Dalhousie University) 

LATIFA BEN HADJ SLIMENE, Université de Sherbrooke
Inference of a Constrained Parameter in Presence of an Uncertain Constraint  [PDF]
We consider a statistical model Xfθ and the problem of estimating θ under the parametric constraint θCRp, with situations where uncertainty resides in the parametric constraint and where we take a simple hierarchical Bayes approach to describe the uncertainty relative to Cand to θ. We will focus on the case of a lower bound constraint. We provide various examples. For estimating a positive normal mean under squared error loss, we obtain hierarchical Bayes estimators which are also minimax. Finally, extensions to predictive density estimation are provided. 
ADAM RAHMAN, University of Waterloo
What Makes a Scatterplot Interesting?  [PDF]
An important question that arises in modern data analytics is how to detect (and ultimately create) interesting structure in a set of points. Tools such as the minimum spanning tree and Delaunay triangulation can help to detect the presence of interesting structure. Using these concepts, Wilkinson and Wills introduced scagnostics, which uses the tools available in graph theory to numerically summarize the structure of a scatterplot in two dimensions. We will consider some of the limitations of scagnostics, propose new measures that capture interesting structure that escapes current scagnostics, and consider the possibilities of generalization to higher dimensions.
YILEI WU, University of Waterloo
Large Covariance Matrix Estimation - A Factor Model Approach  [PDF]
Estimating high-dimensional covariance matrix is a challenging and important problem. Motivated by lasso-type estimators in the literature, we reduce the complexity of the estimation problem by imposing a factor model structure for the population covariance matrix. We prove the consistency of our estimator under moderate conditions on the eigenvalues of the population covariance matrix. Our covariance matrix estimate can be used in various statistical procedures, such as discriminant analysis. 
XIN LIU, Western University
Improve Performance of Support Vector Machine Classifiers with Data Adaptive Kernel  [PDF]
In this talk, a new way to enhance the performance of an SVM classifier is presented. The initial kernel function is conformally re-scaled in an adaptive way so that the separation between two classes can be effectively enlarged, based on the prior knowledge obtained from the conventional SVM. The modified classifier takes into consideration the distribution of the support vectors in the feature space, and the correlation between voxels will be dealt with by selecting only limited numbers of parameters properly. Improvement of prediction accuracy from this data-dependent SVM is shown with numerical studies. 
NATHANIEL STEVENS, University of San Francisco
Comparing the Reliability of Related Populations with the Probability of Agreement  [PDF]
Combining information between different populations to improve precision, simplify future predictions or improve underlying understanding of relationships can be advantageous when considering the reliability of several related sets of systems. Using the probability of agreement to help quantify the similarities of populations can help to give a realistic assessment of whether the systems have reliabilities that are sufficiently similar for practical purposes to be treated as a homogeneous combined population. The new method is described and illustrated with an example involving two generations of a complex system where the reliability is modeled using either a logistic or probit regression model