## Departmental Colloquia## Fall 2007 & Spring 2008 |

August 24, 2007

Dr. Shuxia Sun, Wright State University, Dayton, OH

Title: BOOTSTRAPPING THE EXPECTED SHORTFALL

Abstract: The expected shortfall is a popular risk measure in financial risk management. It is defined as the expected loss given that the loss is greater than a given high quantile. We derive the asymptotic properties of the blocking bootstrap estimators for the expected shortfall of a stationary process under strongly mixing conditions. Results from empirical examples and a small simulation study will also be presented to evaluate the performance of the proposed block bootstrap estimators.

Brief Introduction: Shuxia Sun is an Assistant Professor in the Department of Mathematics and Statis- tics at Wright State University. She completed her Ph.D degree in Statistics in 2004 from Iowa State University. Her research has been mainly focused on non-parametric estimation of time series models and their applications.

September 7, 2007

Dr. Tonghui (Tony) Wang, New Mexico State University

Title:Versions of Cochran's Theorem under Multivariate Settings

Abstract: It is well known that Cochran's theorem related to the distribution of quadratic forms plays an important role in regression, analysis of variance, covariance analysis, linear models, MINQUE theory, etc. Cochran's theorem in its univariate and multivariate versions provides connections between statistics and matrix algebra. In this talk, we will discuss versions of Cochran's theorem for multivariate normal model, for elliptically contoured models, and for skew normal models. Also several research projects in this topic will be addressed in this talk.

September 14, 2007

Prof. S.Ejaz Ahmed, University of Windsor, Canada

Title: Shrinkage and Lasso/Lars and Related Estimation Strategies in Partially Linear Models,

Abstract: In this talk, I consider a partially linear model where the vector of coefficients in the linear part can be partitioned where first sub-vector is the coefficient vector for main effects (e.g. treatment effect, genetic effects) and the other is a vector for ‘nuisance’ effects (e.g., age, lab). In this situation, inference about may benefit from moving the least squares estimate for the full model in the direction of the least squares estimate without the nuisance variables (Steinian shrinkage), or to drop the nuisance variables if there is evidence that they do not provide useful information (pre-testing). We investigate the asymptotic properties of Stein-type and pretest semiparametric estimators under quadratic loss and show that under general conditions a Stein-type semiparametric estimator improves on the full model conventional semiparametric least square estimator. We also consider a LASSO type estimator for partially linear models and give a Monte Carlo simulation comparison of theses estimators. The comparison shows that shrinkage method performs better than LASSO when the number of restriction on parameter space is large.

September 21, 2007

Dr. Jie Chen, University of Missouri- Kansas City

Title: A Change point model approach for detecting significant DNA copy number changes in aCGH data

Abstract: DNA copy number of a region of a genome is the number of copies of genomic DNA in that region. It is biologically known that DNA copy number changes correspond to chromosomal aberrations and signify abnormality of a cell. Cancer (and some other genetic diseases) development is usually relevant to DNA copy number changes on the genome. Modern biomedical technology, such as array Comparative Genomic Hybridization (aCGH), has made it possible to make whole genome copy number maps for a biological study. Therefore, identifying statistically significant DNA copy number changes is evidently crucial in cancer research, clinical diagnostic applications, and other related genomic research. We propose to use a change point model approach to identify statistical significant DNA copy number changes in aCGH datasets. Monte-Carlo simulation and applications of the proposed method on aCGH datasets of several cell lines (fibroblast cancer cell line, breast tumor cell line, and breast cancer cell line) indicate that the proposed method is very powerful in identifying DNA copy number changes.

September 28, 2007

Dr. Craig L. Zirbel, Bowling Green State University

Title: RNA multiple sequence alignment using stochastic context-free grammars and 3D structural data

Abstract: RNA molecules perform a variety of functions in the cells of all living organisms. For example, proteins are assembled by ribosomes, which are primarily made of RNA. Different organisms have slightly different RNA molecules as a result of their different evolutionary histories. The differences appear primarily in the sequence of nucleotides (A, C, G, U) of which the RNA molecule is composed. At the same time these RNA molecules have many common structural features because they play the same functional role in their respective organisms. This leads to a problem of probabilistic modeling: what variability is allowed in the RNA sequence and what variability is not? Stochastic Context-Free Grammars (SCFG) have been used to model variability in RNA sequences for just over a decade, and have been successful in aligning RNA sequences from different organisms in order to infer their structural similarities. In the last few years, 3D crystal structures of entire RNA molecules have become available. We illustrate how to use the wealth of information they give about non-Watson-Crick basepairs and RNA motifs to create highly accurate sequence alignments. Accurate alignments have many uses, for example, inferring the evolutionary tree and the place of each organism in it. 3D structure-based alignments can help us infer 3D structure from sequence data alone, and can help in the search for new RNA molecules in genomic data.

October 12, 2007

Dr. Jared Bronski, University of Illinois at Urbana-Champaign

Title: Defect Eigenvalues and Diophantine conditions via the Evan's function

Abstract: We consider the problem of the Schrodinger equation with a potential consisting of a periodic part plus a compactly supported defect. Such models arise in various optical settings as well as in condensed matter physics as a model for color in crystals impurities. I'll outline a way to count the eigenvalues associated with the defect in terms of the winding number of a one-parameter family of matrices. The real fun comes when we consider the number of eigenvalues in the large energy limit. This turns out to depend on the solvability of a certain Diophantine approximation problem, and so behaves very differently if the width of the support of the defect is rational or irrational.

October 26, 2007

Dr. Corneliu Hoffman, Bowling Green State University

Title: "Groups, Geometries, and Amalgams"

Abstract:

November 2, 2007

Professor Arthur Yeh, ASOR, Bowling Green State University

Title: Statistical Control Charts and Profile Monitoring

Abstract: In the first part of the presentation, I will talk about some of the recent developments in statistical control charts. These include multivariate control charts for monitoring the covariance matrix when sample size is one; control charts for detecting a decrease in variance when sample size is one; and a general methodology for constructing combined charts for simultaneously monitoring multiple population parameters. In the second part of the presentation, I will switch gear to another interesting problem: statistical process control for profile functions. I will start with some existing works and follow up with some recent developments. My intention is to share with you some of the interesting developments in statistical control charts research. Therefore, I will place more emphasis on problem settings and methodologies, and less on numerical evaluations and comparisons of different methodologies.

November 9, 2007

Professor E. Seneta, University of Sydney, Australia

Title: Stochastic Matrices and Google

Abstract: Google utilizes the stationary/limiting distribution of a very large finite stochastic matrix with strictly positive entries to rank responses to a query. The talk will sketch the properties of stochastic matrices, the philosophy leading to the construction of a Google matrix, the evaluation of this left eigenvector, and the manner of Google response to a query. The convergence rate for the evaluation will be presented in terms of a coefficient of ergodicity, which is a scalar expression for the contractive effect of multiplication by a stochastic matrix. This powerful and long-overlooked idea occurs in Markov's first paper on probability chains, published precisely 100 years ago.

November 16, 2007

Dr. Anna Kasikova, Bowling Green State University

Title: Point-line space associated with buildings

Abstract: Buildings are geometric objects introduced by Jacques Tits. They can be defined as simplicial complexes or as chamber systems. Point-line spaces are another kind of geometric objects. I will give a definition of buildings as chamber systems of type a Coxeter matrix $M$ and a definition of point- line spaces. Then I will describe a way of constructing point-line spaces from buildings and state some properties of these point-line spaces.

November 30, 2007

Professor Arjun Gupta, Bowling Green State University

Title: Ubiquitous Success of Gaussian Model and Modeling Skewness

Abstract: In this talk,first a family of skew symmetric distributions will be defined.Then the univariate skew-normal distribution and some of its properties , including the result that the square of a skew-normal random variable is chi-square,will be described. Two applications of this model to the stock returns data and the data on twins will be presented. Then a skew multivariate normal distribution will be defined and its properties will be studied in some details.A stochastic representation of the skew multivariate normal random vector will be given which is useful for computer simulation.Further generalization to the matrix case will be indicated and some unsolved problems in this area will be pointed out.

January 11, 2008

Professor Vic Norton, Bowling Green State University

Title: Sharpe-optimal SPDR portfolios or How to beat the market and sleep well at night

Abstract: The Sharpe Ratio of an investment portfolio is, loosely speaking, the ratio of its reward to its risk. We seek portfolios of maximum Sharpe Ratio from a fixed universe of Exchange Traded Funds (Select Sector SPDRs). It is convenient to look at this problem in a geometric setting. Then a portfolio is identified with its risk vector in a high-dimensional Euclidean space, and the Sharpe Ratio of the portfolio is proportional to the cosine of the angle between the risk vector and an expected-reward axis. Now we seek to maximize this cosine (and thus the Sharpe Ratio).

January 25, 2008

Dr. Xin He, Division of Biostatistics, College of Public Health, The Ohio State University

Title: Semiparametric Analysis of Multivariate Panel Count Data

Abstract: Multivariate panel count data frequently occur in periodic follow-up studies that involve several different types of recurrent events of interest. In many applications, these recurrent event processes can be correlated and it may not be easy to accommodate the dependence structures. In this talk, I will present a class of marginal mean models that leave the dependence structures for related types of recurrent events completely unspecified. Some estimating equations are developed for inference and the resulting estimates of regression parameters are shown to be consistent and asymptotically normal. Simulation studies are conducted for practical situations and the methodology is applied to a motivating cohort study of patients with psoriatic arthritis.

February 8, 2008

Dr. John Chen, Bowling Green State University

Title: Simultaneous Inference for Efficacy and Toxicity

Abstract: In this talk, we will discuss a general nonparametric inference approach to estimate the minimum effective dose and maximum tolerated dose of a drug. The approach is applied to analyze a data set regarding the killing effects of Allicin (a chemical compound in raw garlic) on B-cell lymphocytic leukemia tumor cells in the investigation of molecular cancer therapy.

February 15, 2008

Gary Nonnemacher, Liberty University

Title: Math Service Courses for non-Mathematical Students

Abstract: Three different strategies for strengthening service-course offerings will be discussed. These include modifying traditional courses such as college algebra, using terminal courses such as math for liberal arts, and teaching introductory statistics. Advantages and disadvantages of each strategy will be presented along with some findings and personal experience. Audience participation will be encouraged and a time for questions will follow the presentation.

February 22, 2008

Dr. Wei Ning, Bowling Green State University

Title: A Moment-based Test for the Homogeneity in Mixture Natural Exponential Family with Quadratic Variance Function

Abstract: We propose a simple moment-based procedure for testing homogeneity in the natural exponential family with quadratic variance functions. In literature, solutions to this problem normally involve establishing identifiability of parameters first, then testing the hypotheses whether the data come from a single distribution or a mixture of distributions. Our procedure directly tests the hypotheses without the need to establish parameter estimability. Simulation studies demonstrate that the power of our test is comparable to the supplementary score test and the separate score test proposed by Wu and Gupta (2003), and the normalized score test proposed by Shoukri and Lathrop (1993). In these simulation studies, the methods by the others are specific to cases with a known null distribution, and our methods can also be applied to cases with unknown null distribution. Our test procedure is demonstrated on two real data sets.

March 14, 2008

Dr. Jonathan Hall, Michigan State University

Title: Latin squares and groups with triality

Abstract: Latin squares are simple combinatorial objects arising from the multiplication tables of groups or, more generally, loops. The loop is commutative if the Latin square is symmetric. This in turn corresponds to a duality automorphism of an associated geometry. Such geometries rich in duality automorphisms come from Moufang loops and yield an automorphism group with triality.

March 21, 2008

Professor Joseph Cavanaugh, The University of Iowa

Title: Occam’s Razor and Statistical Model Selection

Abstract: Occam's Razor is a pervasive philosophical principle that has been reflected in the writings of many renowned scholars, including Isaac Newton, Leonardo da Vinci, and Albert Einstein. The principle is often expressed as follows: given two or more competing explanations for a phenomenon, none of which can be discounted, the simplest explanation is to be preferred. Translated to statistical modeling, Occam’s Razor is often referred to as the Law of Parsimony, which claims that no more causes should be assumed than those that will account for the effect. In practice, models with a simplistic structure are often subjectively favored over models with a complex structure, since the former are more easily interpreted. However, from a statistical perspective, do simple models hold an advantage over complex models? The statistical advantage of favoring models that comply with the Law of Parsimony is an improvement in inferential accuracy; in particular, in predictive accuracy. We show that the framework for discrepancy-based model selection criteria provides a paradigm for choosing a model that adheres to Occam’s Razor. We outline the development of this framework. In formulating a criterion, we discuss the importance of estimating a predictive measure known as the expected optimism, which leads to the criterion’s penalty term. The Akaike information criterion and its corrected variants are featured as examples. We argue that model selection criteria may provide a more appropriate basis for model determination than hypothesis testing. To illustrate the utility of selection criteria, we consider applications based on an Australian coronary heart disease study and the Iowa Fluoride Study.

March 28, 2008

Professor Robert Ochs, University of Toledo

Title: An extension of the dynamics of one-dimensional wave splitting to three dimensions via Clifford algebra

Abstract: A review of the Green function approach to one-dimensional direct and inverse scattering for the wave equation using split waves will be presented. After a discussion of previous attempts at extensions to three dimensions, the dynamics of split fields in one dimension are extended to three dimensions using Clifford algebra. The solutions of the resulting equations provide insight into the effectiveness of the wave splitting approach and may be useful in solving the three-dimensional inverse scattering problem in the time domain.

April 11, 2008

Dr. Brisa Sanchez, School of Public Health, University of Michigan

Title: Residual-based diagnostics for structural equation models

Abstract: Classical diagnostics for structural equation models are based on aggregate forms of the data and are ill suited for checking distributional or linearity assumptions. We extend recently developed goodness of fit tests for correlated data based on subject-specific residuals to structural equation models with latent variables. The proposed tests lend themselves to graphical displays and are designed to detect misspecified distributional or linearity assumptions. To complement graphical displays, test statistics are defined; the null distributions of the test statistics are approximated using computationally efficient simulation techniques. The properties of the proposed tests are examined via simulation studies. We illustrate the methods using data from a study of in-utero lead exposure.

April 18, 2008

Professor Andre Boivin, The Univerisity of Western Ontario, Canada

Title: Uniform approximation on Riemann surfaces: a survey

Abstract: The qualitative theory of uniform approximation by holomorphic (think: polynomial) or meromorphic (think: rational) functions on compact subsets of Riemann surfaces is relatively well-understood. We have now complete characterizations of those compacts sets on which approximation is always possible. When replacing compact sets by closed but not necessarily bounded sets, very little is known, except in the planar case. I intend to present a survey of the theory, including recent results and open problems.