UCF Math Department's
Probability and Statistics Seminar
Spring 2010

Fridays in MAP 213 from 2:30 PM - 3:30 PM, unless otherwise noted.

Organized by Jason Swanson

Past Seminars

Schedule and Abstracts

We consider systems of negative point charges inside a jellium of uniform positive charge on the tube $[-A,B]\times[-\pi,\pi]$. Let $N(x,\omega)$ denote the signed charge imbalance up to $x$, i.e., on the space $[-A,x]\times[-\pi,\pi]$. We bound the probability of $|N(0)|>\lambda$ uniformly in $A$ and $B$ and show that this probability goes to $0$ as $\lambda\to\infty$. Symmetry breaking follows from a result of Aizenman, Goldstein, Lebowitz (2001).

Self-consistency principle, originated by Efron (1967), generalizes MLE for semi/non-parametric estimation with incomplete data and under an arbitrary loss function. It is conceptually appealing, essentially a mathematical formalization of the common-sense “trial-and-error" methods; mathematically elegant, with one fixed-point equation to solve and a general contraction mapping theorem to establish its optimality; and practically straightforward because it directly uses a complete-data method (e.g., LASSO, kernel density estimation) within iterations, much like the EM algorithm. Its major disadvantage is that it can be computationally very intensive. However, increasingly efficient (approximate) implementations are being discovered, such as for wavelet de-noising with hard and soft thresholding. This talk summarizes these findings, based on joint work with Thomas Lee and Zhan Li.

Few paradoxes have impacted everyday life more than Simpson’s Paradox has. Yet paradoxically, Simpson’s paradox is not even a paradox in the mathematical sense. Simple arithmetic can easily show that it is possible for a surgeon to have the highest overall success rate, and yet have the lowest success rates for each type of surgeries he performed. The fact that you may feel this phenomenon counterintuitive is precisely the reason that the Simpson’s paradox has led to many erroneous conclusions and decisions that affect people’s life, particularly those from social and medical studies, where comparisons using aggregated data are routinely performed. This talk demonstrates the danger of Simpson’s paradox via a number of real-life examples, from the famous Berkeley sex bias case to measuring disparity in mental health service based on the recently released National Latino and Asian American Study (NLAAS), and from batting averages and to the most recent debate on unemployment rates (Wall Street Journal, December 2, 2009). No statistical background is required to understand this talk, but only some common sense and a desire to think deeply beyond formulas.

A great deal of the statistical literature deals with a single sample coming from a distribution, univariate or multivariate, and the problem is to identify the distribution or parts thereof by an array of estimation and testing procedures. As such, this practice neglects to bring in information from other sources which could improve the desired inference. An approach which fuses information from many sources will be presented and applied in US mortality rate prediction.

For complete details, please visit http://math.swansonsite.com/ssp2010/.

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of selected portfolios among a vast pool of assets, as demonstrated in Fan et. al. (2008). The required high-dimensional volatility matrix can be estimated by using high frequency financial data. This enables us to better adapt the local volatilities and local correlations among vast assets and to increase significantly the sample size for estimating the volatility matrix. This paper studies the volatility matrix estimation using high-dimensional high-frequency data from the perspective of portfolio selection. Specifically, we propose the use of ``pairwise-refresh time" and ``all-refresh-time" methods proposed by BHLS (2008) for estimation vast covariance matrix and compare their merits in the portfolio selection. We also establish the large deviation results of the estimates, which guarantee good properties of the estimated volatility matrix in vast asset allocation with gross exposure constraints. Extensive numerical studies are made via carefully designed simulation studies. Comparing with the methods based on low frequency daily data, our methods can capture the most recent trend of the time varying volatility and correlation, hence provide more accurate guidance of the portfolio allocation of the next time period. The advantage of use high-frequency data is significant in our simulation and empirical studies, which consist of 30 Dow-Jones stocks and 100 of SP500 components.