October 30, 2:00-3:00pm, 796 COE (Colloquium)
Professor Hongtu Zhu
University of North Carolina at Chapel Hill
Intrinsic Regression Models for Medial Representation and Diffusion Tensor Data
In medical imaging analysis and computer vision, there is a growing interest in analyzing various manifold-valued data including 3D rotations, planar shapes, oriented or directed directions, the Grassmann manifold, deformation field, symmetric positive definite (SPD) matrices and medial shape representations (m-rep) of subcortical structures. Particularly, the scientific interests of most population studies focus on establishing the associations between a set of covariates (e.g., diagnostic status, age, and gender) and manifold-valued data for characterizing brain structure and shape differences, thus requiring a regression modeling framework for manifold-valued data. The aim of this talk is to develop an intrinsic regression model for the analysis of manifold-valued data as responses in a Riemannian manifold and their associations with a set of covariates, such as age and gender, in Euclidean space. Because manifold-valued data do not form a vector space, directly applying classical multivariate regression may be inadequate in establishing the relationship between manifold-valued data and covariates of interest, such as age and gender, in real applications. Our intrinsic regression model, which is a semiparametric model, uses a link function to map from the Euclidean space of covariates to the Riemannian manifold of manifold data. We develop an estimation procedure to calculate an intrinsic least square estimator and establish its limiting distribution. We develop score statistics to test linear hypotheses on unknown parameters. We apply our methods to the detection of the difference in the morphological changes of the left and right hippocampi between schizophrenia patients and healthy controls using medial shape description.
October 16, 3:00-4:00pm, 796 COE
School of Mathematics, Georgia Institute of Technology
Empirical Likelihood Method For Conditional Value-at-Risk
Value-at-Risk is a simple, but useful measure in risk management.
When some volatility model is employed, conditional Value-at-Risk is of importance.
As ARCH/GARCH models are widely used in modeling volatilities, in this talk,
we first propose empirical likelihood methods to construct confidence intervals for
the conditional Value-at-Risk with the volatility model being an ARCH/GARCH model.
We further consider an empirical likelihood-based estimation
of the conditional Value-at-Risk in the nonparametric regression model.
October 9, 3:00-4:00pm, 796 COE
Dr. Zhipeng Cai
Mississippi State University
Association Study on Pedigree SNP Data
Most association study methods become either ineffective or inefficient when dealing with increasing numbers of SNPs. Suggested by the block-like
structure of the human genome, a popular strategy is to use haplotypes to try to capture the correlation structure of SNPs in regions of little recombination.
This haplotype based association study would have significantly reduced degrees of freedom and be able to capture the combined effects of tightly linked causal variants. An efficient rule-based algorithm is presented for haplotype inference from pedigree genotype data, with the assumption of no recombination.
This zero-recombination haplotyping algorithm is extended to a maximum parsimoniously haplotyping algorithm in one whole genome scan to minimize the total number of breakpoint sites. We show that such a whole genome scan haplotyping algorithm can be implemented in O(m3n3) time in a novel incremental fashion, here m denotes the total number of SNP loci on the chromosome. Extensive simulation experiments using eight pedigree structures that were used previously for association studies showed that the haplotype allele sharing status among the members can be deterministically, efficiently, and accurately determined, even for very small pedigrees.
October 2, 3:00-4:00pm, 796 COE
Professor Yixin Fang
Georgia State University
Some discussion on variable selection in mixed-effects models
For model selection in mixed effects models, Vaida and Blanchard (2005) demonstrated that the marginal Akaike
information criterion is appropriate as to the questions regarding the population and the conditional Akaike
information criterion is appropriate as to the questions regarding the particular clusters in the data. This paper
shows that the marginal Akaike information criterion is asymptotically equivalent to the leave-one-cluster-out
cross-validation and the conditional Akaike information criterion is asymptotically equivalent to the
September 25, COE 2:00-3:00pm, 796 (Colloquium)
James L. Kepner, PhD
Vice-President, Statistics and Evaluation
American Cancer Society
Adjunct Professor, Department of Biostatistics
Rollins School of Public Health
Survey of Exact Methods in Sample Size Determination
Discussed are exact one-stage and group-sequential sample size determination methods for one- and two-sample binomial proportions testing problems, methods for the corresponding finite population tests, and simultaneous tests for correlated binomial proportions. Design properties are discussed and new/unpublished results are described. The exact group sequential methods allow early stops only for efficacy or only for futility or for either efficacy or futility. Sample sizes, levels of significance and power at fixed points in the research hypothesis parameter space are compared among competing designs including those derived using asymptotic normal theory methods. Documents provided will include
a description of how sample points are placed in the rejection region,
simple proofs for each of the 3 one-sample theorems,
tables demonstrating the efficiency of the two-sample designs,
a table showing how close the one-sample designs can get to the one-stage uniformly most powerful test in terms of significance and power,
a table demonstrating the remarkable sample size savings if two or more binomial endpoints are tested simultaneously.
September 23, 2:30-3:30pm, 796 COE (Colloquium)
Professor Yufeng Liu
Department of Statistics & Operations Research,
Carolina Center for Genome Sciences,
University of North Carolina at Chapel Hill
Estimation of Multiple Noncrossing Quantile Regression Functions
Quantile regression is a very useful statistical tool to learn the
relationship between the response variable and covariates. For many
applications, one often needs to estimate multiple conditional quantile
functions of the response variable given covariates. Although one can
estimate multiple quantiles separately, it is of great interest
to estimate them simultaneously. One advantage of simultaneous estimation is that multiple quantiles can share strength among them to gain betterestimation accuracy than individually estimated quantile functions. Another important advantage of joint estimation is the feasibility to incorporate noncrossing constraints of quantile regression
functions. In this talk, I will present a new multiple noncrossing
quantile regression estimation technique. Both asymptotic properties and
finite sample performance will be presented to illustrate usefulness of
the proposed method.
August 28, 2:00-3:00pm, 654 COE (Colloquium)
Professor Dabao Zhang
Department of Statistics, Purdue University
Penalized orthogonal-components regression for large p small n data
We propose a penalized orthogonal-components regression
(POCRE) for large p small n data. Orthogonal components are sequentially constructed to maximize, upon standardization, their correlation to the response residuals. A new penalization framework, implemented via empirical Bayes thresholding, is presented to effectively identify sparse predictors of each component. POCRE is computationally efficient owing to its sequential construction of leading sparse principal components. In addition, such construction offers other properties such as grouping highly correlated predictors and allowing for collinear or nearly collinear predictors. With multivariate responses, POCRE can construct common components and thus build up latent-variable models for large p small n data. This is joint work with Yanzhu Lin and Min Zhang.
May 8, 2:00-3:00pm, 796 COE
Professor Xiaoli Gao
Department of Mathematics and Statistics at Oakland University
On the study of penalized LAD methods
Penalized regression has been widely used in high-dimensional data
analysis. Much recent work has been
done on the study of penalized least squares methods. In this talk, I
will first introduce the application of penalized LAD
methods in detecting copy number variations. I will then discuss some
theoretical properties of penalized LAD methods in high-dimensional
settings. The finite sample performance of proposed methods are
demonstrated by simulation studies.