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In a first attempt to study urns growing under rules concerning choices of fixed-size multisets of balls, we investigate the evolution of an urn of colored balls where one chooses a pair of balls and observes rules of ball addition according to the outcome. A non-square ball addition matrix corresponds to such a scheme, in contrast to Polya urn models that possess a square ball addition matrix. We look into the case of constant row sum and identify a balanced case therein, where one gets an asymptotic normal distribution for the number of balls of any color via martingale theory.

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Title: Ordered Multivariate Extremes
SPEAKER: Professor SARALEES NADARAJAH
Department of Statistics
University of California at Santa Barbara
DATE: September 22, 2000
LOCATION: Funger Hall 308
TIME: 11:00 a.m.

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In recent years statistical extreme value theory has matured to such an extent to contribute usefully to the study of substantial real problems, particularly in the area of environmental extremes. Examples include the design of off-shore structures (Coles and Tawn, 1994) and

the study of reservoir flood safety (Anderson and Nadarajah, 1993). A fairly commonly occurring characteristic is that the variables whose extremes are of interest are ordered. In hydro-meteorology one thing that is of interest is the dependence of extreme values of d-hour rainfall over a range of values of d. One approach is to fit a multivariate extreme value distribution over that range. If X(d) denotes rainfall aggregated over d hours, and if d' > d then X(d) <= X(d')<= (d'/d) X(d) for all (X(d), X(d')), so an order restriction in the multivariate extreme value model is needed. Similar order restrictions arise in the study of the joint distributions of large hourly mean wind speeds and large wind gusts. The aim of this talk is to develop multivariate extremal models and associated statistical procedures for vector observations whose components are subject to an order relationship. We consider only the bivariate case. The results are applied to the joint analysis of rainfall extremes corresponding to different durations.

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Title: AN IN-DEPTH PROBABILISTIC ANALYSIS OF QUICKSORT
SPEAKER: Professor James Fill
Department of Mathematical Sciences
The Johns Hopkins University
DATE: September 29, 2000
LOCATION: Funger Hall 308
TIME: 11:00 a.m.

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Quicksort, the standard sorting procedure in Unix systems, is probably the most widely used general-purpose sorting algorithm, and has been the subject of intense analytic and numerical study. I will present the most in-depth probabilistic analysis of the running time of Quicksort to date.In particular, I will discuss how to extend the contraction method of Uwe Roesler and (independently) Ludger Rueschendorf to obtain Berry-Esseen-type results about the rate of convergence to its limiting distribution of the (suitably centered and scaled) number of comparisons required to sort a file of n keys; Wasserstein (or Mallows) and Kolmogorov-Smirnov metrics both play a role in this regard. The limiting distribution itself (call it F) is a bit nebulous: it is known only as the unique fixed point with finite variance of a certain distributional identity. I will show how to use Fourier analysis to prove that F has an everywhere positive and infinitely differentiable density f, and that each derivative f^{(k)} enjoys superpolynomial decay in each tail. In particular, each derivative is bounded. I will also discuss how to obtain explicit bounds on the error in (rapid) numerical approximation of F and its derivatives (and related functionals). If time permits, I will also discuss perfect simulation from F, and/or discuss large deviations, and/or explain how the same sort of program can be carried out for other divide-and-conquer recurrences.

(This is joint work with Svante Janson of Uppsala University in Sweden.)

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Title: Challenges in Conducting Surveys of Businesses
SPEAKER: Carol Caldwell
The Census Bureau
DATE: October 6, 2000
LOCATION: Funger Hall 307
TIME: 3:00 p.m.

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The U.S. Census Bureau conducts over 20 major surveys of businesses that are used to measure U.S. economic activity. These surveys present interesting challenges in survey design, sampling, imputation, estimation, and variance estimation. This talk will highlight key issues involved in conducting surveys of businesses, and will present some recent examples of survey improvements implemented at the Census Bureau.

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Title: ON PROPERTIES OF MULTI­DIMENSIONAL STATISTICAL TABLES
SPEAKER: Dr. Lawrence H. Cox
U.S. Environmental Protection Agency
DATE: October 13, 2000
LOCATION: Funger Hall 308
TIME: 11:00 p.m.

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Statistical data are often organized in tabular form. Count data are nonnegative integers, and often magnitude data are made to take nonnegative integer values. Two­dimensional tables enjoy mathematical properties on which important statistical methods depend, e.g., for stratified sampling, imputation, disclosure limitation, and sampling and fitting log­linear models to contingency tables. We demonstrate that many of these desirable mathematical properties, and consequently their associated statistical methods, are not extendible to three or higher dimensions. We demonstrate that ill­behaved examples are ubiquitous, abundant and consequently not mathematical anomalies. To address these shortcomings, we provide necessary and sufficient conditions and an empirical test for the existence of an n­dimensional table with prescribed (n­1)­dimensional marginal totals (feasibility) and a complete characterization of n­dimensional tables for which the existence of integer­valued entries and associated optima are assured (integrality).

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Title: Statistical Issues in Genetic Studies Using Multiple Closely Linked Markers
SPEAKER: Professor Hongyu Zhao
Division of Biostatistics, Yale University School of Medicine

DATE: October 19, 2000
LOCATION: Funger Hall 308
TIME: 4:30 p.m.
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With the rapid progress in the Human Genome Project, it is becoming a reality to study all genetic

variations in humans simultaneously. These technological advances have created both exciting and challenging opportunities for statisticians to develop novel statistical tools to take advantage of the large amount of biological information generated from this biological evolution. In this talk, I will discuss three topics related to the use of large numbers of genetic markers:

Population genetics studies on linkage disequilibrium patterns among many closely linked genetic markers;
Linkage disequilibrium mapping of disease genes using genotype data from case-control studies;
Family-based association studies using multiple tightly-linked markers.
For each topic, I will describe the biological background, types of genetic data that are utilized to address the biological questions, limitations of the current statistical methods, and novel statistical methods under development.

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Title: Introduction to population pharmacokinetics/pharmacodynamics (PK/PD) analysis

SPEAKER: Mr. Xuejun Chen
Department of Statistics
George Washington University

DATE: November 3, 2000
LOCATION: Funger Hall 307
TIME: 3:00-4:00 p.m.
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Pharmaceutical industry scientists and the FDA have long been interested in the use of population pharmacokinetics/pharmacodynamics in the analysis of drug safety and efficacy. Using the population PK approach in drug development offers the possibility of gaining integrated information on pharmacokinetics, not only from relatively sparse data from study subjects, but also from relatively dense data or a combination of sparse and dense data. This talk will give brief description of statistical background of population PK/PD analysis (nonlinear mixed-effects model), comparison between traditional PK/PD analysis and population PK/PD analysis and procedure for population PK/PD model development.

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Title: A New Look at Exponential Smoothing

SPEAKER: Professor Keith Ord
McDonough School of Business,
Georgetown University

DATE: November 10, 2000
LOCATION: Funger Hall 613
TIME: 12:00-1:00 p.m.
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Exponential Smoothing (ES) forecasting methods are widely used but are often discussed without recourse to a formal statistical framework. We consider a variety of time series models that may be used to generate predictive distributions for ES forecasts. This class includes ARIMA and (non-linear) structural models, which helps to explain the robustness of ES in forecasting applications. In particular, we examine Single Source of Error (SSOE) structural models that allow ready extension to non-linear processes. GARCH-type models for SSOE schemes will be briefly considered.

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Title: Spectral Analysis of Fractal Noise

SPEAKER: Professor Sherry Scott
Department of Statistics,
George Washington University

DATE: December 1, 2000
LOCATION: Funger Hall 307
TIME: 3:30-4:30 p.m.
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The term fractal noise is commonly used to refer to signals whose measured spectra obey a power law decay of fractional order. The processes used to model this (fractal) behavior are in turn called fractal processes. Fractal noise or signals occur in a wide range of phenomena including biomedical, weather and economic data. Yet, the spectral analysis of these signals remains unresolved. In this talk, we introduce the Wiener-Wintner theorem, a generalized harmonic analysis result concerning a signal and its power spectrum, to the spectral analysis of fractal noise.

We shall concentrate on the 1/f - family of fractal noise in which case the empirical spectra have decay on the order k with 0 < k < 2. Our approach will progress from a statistically-based perspective to a deterministic point of view, as we consider the following topics:

(1) a generalized power spectrum; (2) a characterization of second order properties via the wavelet transform; (3) a wavelet-based representation of 1/f processes; and (4) an extension of the Wiener-Wintner theorem to 1/f noise.

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Title: Is the Wilson-Hilferty Transform a Modern Method?

SPEAKER: Professor George R. Terrell
Department of Statistics
Virginia Polytechnic Institute and State University

DATE: December 8, 2000
LOCATION: Funger Hall 307
TIME: 3:30-4:30 p.m.
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In 1931 Wilson and Hilferty discovered a quick, rough method for obtaining p-values for chi-squared statistics. Its usefulness declined with the advent of computers. Recently there has been interest in "saddlepoint" methods for approximate probability calculations. These are fairly general, and can therefore often be adapted to the ever more complicated test statistics that modern statisticians use. However, they do not as readily provide confidence intervals and simulated values as does a Wilson-Hilferty transform. We will propose a generalized Wilson-Hilferty transform, and establish that it is almost a saddlepoint method. The method therefore combines traditional and modern virtues, and shows promise for difficult inference problems.

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The contact person is Reza Modarres at Reza@gwu.edu

or 202-994-6359.