UMKC Mathematics Graduate Seminar Series

Graduate Seminar Series — Fall 2009

Location: Haag Hall, rm 306 (Unless otherwise noted)
Day & Time: Wednesdays or Fridays, 2:00-2:50 pm (Unless otherwise noted)
Campus Map for Talks (PDF Format)

Organizer: Dr. Liana Sega, 235-2849
Email: segal@umkc.edu

Dates, Titles, Speakers (with Abstracts as available)

Friday, Sept. 11
Basic Notions of Control Theory for Linear Time-Invariant Systems
Miron Bekker, Department of Mathematics and Statistics, UMKC

We discuss notions of controllability, observability, transfer functions, and related statements for linear finite dimensional time invariant systems.
Friday, Sept. 18
Response-adaptive Designs: some reflections and some results
Nancy Flournoy, Department of Statistics, University of Missouri

In response-adaptive designs, decisions about the experimental process are made based on accruing observations as trials accumulate. Response-adaptive procedures have a rich history both hypothesis testing and estimation situations. In some, accruing information is primarily used in deciding stop the experiment. In others, treatment allocation probabilities are altered, for example, to favor the better treatment or to stay away from toxic doses. Such procedures are becoming increasingly popular. This talk will provide a brief survey of the field, with a focus that is admittedly biased by the author's own interests.
Wednesday, Sept. 30
Robust Estimation for Randomized Play the Winner Design
An-Lin Cheng, School of Nursing, UMKC

Randomized play the winner design, an adaptive design for clinical trials that is aimed at allocating more patients to a better performing treatment, has received much attention lately. Minimum Hellinger distance methodology has been studied in several settings such as i.i.d. data, Markov chain data, and branching processes data. It has been shown that in these settings the methodology yields "robust" and "efficient" estimates at the model. In this talk, we will describe Minimum Hellinger Distance method of estimation for data accrued using the randomized play the winner design. We will also describe a novel one-step Monte-Carlo approximation for calculating these estimators. We will examine the asymptotic and coverage properties of our method using a "semi-parametric" bootstrap methodology. We will illustrate our results using data from a clinical trial conducted by Eli-Lilly and company.
Friday, Oct. 9
Online Monitoring a Large Number of Data Streams
Yajun Mei, School of Industrial and Systems Engineering, Georgia Institute of Technology

In the modern information age one often monitors a large number of data stream with the aim of offering the potential for early detection a "trigger" event, e.g., biosurveillance and signal detection. In this talk, we are interested in the scenario in which we do not know when the event will occur or which subset of data streams will be affected by the event. Two families of scalable monitoring schemes are proposed based on the sum of the local CUSUM statistics that are "large" under either hard thresholding or top-r thresholding rules. Both are shown to possess certain asymptotic optimality properties.
Friday, Oct. 16
A mathematical model for multi-name credit based on community flocking
Kiseop Lee, Department of Mathematics, University of Louisville

We present a new mathematical model for multi-name credit which employs stochastic flocking. Flocking mechanisms have been used in a variety of models of biological, sociological and physical aggregation phenomena. As a direct application of a flocking mechanism, we introduce a credit risk model based on community flocking for a credit worthiness index (CWI). Correlations between different credit worthiness indices are explained in terms of an interaction rate from the flocking system. Based on the flocking model for CWI, we provide a credit curve for individual names and a default time distribution. We study how to price credit derivatives such as a credit default swap (CDS) and a collateralized debt obligation (CDO) with the proposed model.
Friday, Oct. 23
Bayesian Data Analysis for Ordinal Data
Fanglong Dong, Department of Mathematics and Statistics, UMKC

Bayesian statistics is an important part of statistics and it provides another angle of statistics. Ordinal data are every common in daily life such as the student's grade. We can easily fit a logistic regression model on this type of data, however, we are not sure how to define residual from a frequentist's perspective thus we are unable to detect outlier. Recent research try to solve this problem but not perfectly solved because the dimension of the estimated probabilities falling in every category form a vector. We try to look at this question from a Bayesian perspective by using the idea of latent variable. With the help of latent variable, we can successfully detect outlier. I will talk briefly about the idea of Bayesian thinking and how can we apply Bayesian statistics to ordinal data analysis.
Wednesday, Nov. 4
A matroidal phenomenon of transforming graphs and matrices into balanced structures
Lavanya Kannan, Stowers Institute for Medical Research

A graph G is said to be 1-balanced if for any non-trivial subgraph H of G, we have |E(H)|/(|V(H)|-1) ≤ |E(G)|/(|V(G)|-1). A 1-balanced graph is regarded as a minimally vulnerable network since a knowledgeable enemy (ignoring edge-connectivity) would find no edge set attractive to attack. In this talk, I will present a method to systematically transform any given graph into a 1-balanced graph. Recently, this result has been extended to any general matroid, graphs being a specific type of matroid. Another well-known example of matroids is the representable matroid defined on the columns of the matrices. We will see how a definition of balanceness can be given to matrices and how we may transform any given matrix into a balanced matrix via elementary column operations. We will also see (if time permits) that all these results can be given in the terminology of matroids.
Friday, Nov. 13
Training or Search? Evidence and an Equilibrium Model.
Jun Nie, Federal Reserve Bank of Kansas City

Training programs are a major tool of labor market policies in OECD countries. I use a unique panel data set on the labor market experience of individual German workers between 2000 and 2002 to estimate a dynamic model of search and training, which allows me to quantify the impact of training programs and unemployment benefits on employment, unemployment, output, and the government expenditures.

The model extends Ljungqvist and Sargent (JPE, 1998) by incorporating a training decision and a broader menu of unemployment benefits. I use the Simulated Method of Moment to estimate the structural model. To circumvent the non-smooth and local optima problem in the computation of classical extremum estimators, I implement the Laplace type estimator (LTE) approach recently proposed by Chernozhukov and Hong (2005). The model can match the observed distribution and transitions among different labor market status as well as important wage earning moments conditional on different unemployment experience.

I use the model to quantitatively study the recent reforms implemented in Germany and run more counterfactual experiments. I simulate the transition path under back-to-back unexpected reforms in 2003-2006 and find the dynamics of the models unemployment rates are close to the data. In a counterfactual experiment in which I model an economy with a German-like training system and a US-like unemployment benefit structure (roughly, benefits are lower), I find that employment and output rise substantially.

Department of Mathematics and Statistics