University of Washington - Department of Statistics
R. Douglas Martin
Research at the Interface beteen Statistics and Finance
An Example: Optimal Portfolios and their Sensitivity to Outliers Statistics plays a basic role in finance research, and applications in the finance industry have very large economic implications. At the same time, opportunities for research at the interface between finance and statistics have been largely ignored. In this presentation I will very briefly describe one of the most fundamental problems in finance from a statistical perspective: Constructing an "optimal" portfolio in the sense of mean-variance efficiency. I will describe the constrained optimization problem, state its solution and point out the common statistical estimation problem it poses, namely estimation of a mean vector and a covariance matrix. Then I discuss the issue of outliers and their influence, and indicate how the influence function from statistics might be used to explore sensitivity to outliers. The material is presented primarily to provide a sense of the strong interplay between fundamental aspects of finance and statistics, and to hint at the potential for interesting research at the interface between finance and statistics.
Classification of Acoustic Signals
The problem of classifying acoustic signals arises in many fields of Science and Engineering. Speech recognition, bird-song segmentation and labeling, and discrimination of vibration patterns on industrial machinery are a few examples. In this talk I will give a brief overview of "recent" efforts concerning the bird-song recognition problem. The goal is to give you a general idea of the kind of data and methods involved in acoustic-signal classification problems.
A Likelihood-Based Approach to Cross-Covariance Problems
Cross-covariance problems arise in the analysis of multivariate data that can be divided naturally into two blocks of variables, [X.1, ... , X.p] and [Y.1, ... , Y.q], observed on the same units. In a cross-covariance problem we are interested, not in the within-block covariance, but in the way the Y's vary with the X's. Such problems occur in many fields, including information retrieval, behavioral teratology, meteorology, and chemometrics. The method currently in use for this class of problems, Partial Least Squares (PLS), is computationally stable and yields coefficients which can readily be interpreted. PLS is not based on a likelihood, however, and consequently there is no principled way to perform inference or to compare models with PLS. Methods developed for general structural equation models (SEMs) are likelihood-based, but they are unsuitable for cross-covariance problems. In the current work a likelihood-based model is specified, along with a procedure for maximum-likelihood estimation. The procedure, unlike those based on SEMs, exploits the distinctive properties of the cross-covariance problem. Initial results, from an application to simulated data, are promising.
Wine and Cheese reception to follow in the Statistics lounge, 3rd floor, Padelford.