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Slideshow

Tags: Colloquium Series

The Statistics Department hosts weekly colloquia on a variety of statistcal subjects, bringing in speakers from around the world.

There are now several methods for constructing confidence intervals for prediction accuracy in high dimensional settings. But these methods have high computational cost and are cumbersome to implement. As a result, these types of intervals are rarely reported, and their properties are not well understood. In this talk, we review these methods, one in some detail, and introduce current work which utilizes a mathematical modeling approach to try…
We are concerned with how to select significant variables in semi-parametric modeling. Variable selection for semi-parametric regression models consists of two components: model selection for nonparametric components and selection of significant variables for parametric portion. Thus, it is much more challenging than that for parametric models such as linear models and generalized linear models because traditional variable selection procedures…
With the advance of biotechnology, massive "omics" data, such as genomic and proteomic data, become rapidly available in population based studies to study interplay of genes and environment in causing human diseases. An increasing challenge is how to analyze such high-throughput "omics" data, interpret the results, make the findings reproducible. We discuss several statistical issues in analysis of high-dimensional "omics" data in population…
Functional data analysis has received considerable recent attention and a number of successful applications have been reported. In this paper, asymptotically simultaneous confidence bands are obtained for the mean function of the functional regression model, using piecewise constant spline estimation. Simulation experiments corroborate the asymptotic theory. The confidence band procedure is illustrated by analyzing the CD4 cell counts of HIV…
The sequential Monte Carlo (SMC) methodology has shown a great promise in solving a large class of highly complex inference and optimization problems. Although it was originally designed to solve on-line filtering and smoothing of non-linear non-Gaussian state space models, it has been shown to be equally powerful in dealing with fixed-dimensional problems, utilizing a sequential decomposition principle. In this talk we discuss issues and…
Advances in DNA sequencing, genotyping, and microarray technologies are providing new opportunities in all areas of biology. The rate of data increase and cost decrease over the past 2 decades has exceeded Moore's law, resulting in ever larger datasets in the hands of increasing numbers of researchers. Thus, the need for new statistical and other analytical tools is increasing tremendously. I will present information about the types of genetic…
Penalized splines are a popular method for nonparametric function estimation in partial linear generalized regression models. Constrained versions are presented in this talk, which are useful if the function is known to be increasing or convex. The shape assumptions often fall into the category of a priori knowledge, but occasionally the research question might concern the shape. A model-selection criterion for determining if the constraints…
We propose a cross-validated version of the design-based variance estimator of survey estimators, and describe its use in several survey applications. The estimator is based on the same "leave-on-one" principle as traditional cross-validation, but takes the design effects on the variance into account. We apply the cross-validated estimator as a design-based model selection tool for regression estimators, and show that it is effective in…
A penalized polynomial spline method will be introduced for simultaneous model estimation and variable selection in additive models. The proposed method approximates the nonparametric functions by polynomial splines, and minimizes the sum of squared errors subject to an additive penalty on norms of spline functions. This approach sets estimators of certain function components to exactly zero, thus performing variable selection. Under mild…
The use of economic and statistics principles have been instrumental in developing many quantitative methodologies in finance, for example the famous formula of Black-Scholes that led to a Noble Prize in economics. In order to research in mathematical finance, it is essential to understand both economic principles and the ever changing financial activities in the market. The purpose of this presentation is to find a closed from formula to value…

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