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In many practical settings the independence assumptions for central limit
theorems and strong laws do not hold. What can one do when standard
probability theory does not work?
By looking at super moment generating functions (generating functions
that generate sequence of moment generating functions) one can get a lot
of mileage even in the presence of adverse conditions like strong
dependence. Such super moment generating functions are bivariate, often
satisfying functional equations of non-standard types. Analytic techniques
for squeezing out information (limiting distributions, asymptotic moments,
etc.) involve studying singularities of transforms of these bivariate
functions.

A case study from coin-flipping contests will be presented to show how
analytic techniques are used to prove the non-existence of a limit
distribution for an associated random variable owing to the presence of
periodic fluctuations.
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TITLE: Weighted Likelihood Estimating Equations: The Discrete
Case with Applications to Logistic Regression
SPEAKER: Marianthi Markatou
Department of Statistics
Columbia University
DATE: October 2, 1998
LOCATION: 322 Funger Hall
TIME: 2:00 p.m.

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We will discuss a method for weighting the likelihood equations with the
aim of obtaining fully efficient and robust estimators. We
discuss the case of discrete probability models using several weighting
functions. If the weight functions generate increasing residual
adjustment functions then the method provides a link between the
maximum likelihood score equations and minimum disparity estimation, as
well as a set of diagnostic weights and a goodness of fit criterion.

The equations have multiple solutions. The number of solutions depends on
the amount of mixing or contamination in the population, on the power of
the weights and on the separation between the populations. Those different
roots have diagnostic value for the composition of the population under
study.

The weight functions discussed in this paper do not automatically
downweight a proportion of the data; an observation is significantly
downweighted only if it is inconsistent with the assumed model.

We apply our results to several discrete models. In addition a toxicology
experiment illustrates the method in the context of logistic regression.
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TITLE: STATISTICS IN ENVIRONMENTAL DECISION MAKING: THEY REALLY DO COUNT! SPEAKER: Barry Nussbaum U.S. Environmental Protection Agency Washington, D.C. DATE: October 16, 1998 LOCATION: 309 Funger TIME: 2:00 pm --------------------------------------------------------------------- Despite the cynicism, statistics are used in the decisions made on environmental policy, regulations, and enforcement actions. However, it is frequently the effectiveness of the presentation of the statistics, rather than the raw statistics, that make the difference. Several general guidelines are explored; and then three specific examples in which the author was personally involved are discussed. One ended up in a regulation, one in court, and one on the desk of the President of the United States. In more recent developments, the EPA has set up a Center for Environmental Information and Statistics that will disseminate environmental statistics and data for public access. The paper discusses the role that this Center and its data dissemination plays in current decision-making. ---------------------------------------------------------------------

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TITLE: Evaluating Cancer Biomarkers SPEAKER: Stuart Baker National Cancer Institute Bethesda, Maryland DATE: November 6, 1998 LOCATION: 309 Funger TIME: 11:00 am ---------------------------------------------------------------------- Many long-term clinical trials and cohort studies involve the repeated collection and storage of tissue and serum specimens. In random samples of cases and controls, investigators test the specimens for various molecular markers for cancer. An important question is what combination, if any, of the molecular markers at various times should be studied in a future trial as a trigger for early intervention. To answer this question, we propose using logistic regression combined with a simple utility function to create what we call an adjusted ROC curve. The adjusted ROC curve plots the true positive rate against the number of unnecessary biopsies per cancer death prevented such that the lower bound of the utility function equals zero. We apply the methodology to data on prostate specific antigen (PSA), a possible marker for prostate cancer, collected at two times as part of the Alpha-Tocopherol Beta Carotene Lung Cancer Prevention Trial (ATBC study). We also discuss the computation of sample size. --------------------------------------------------------------------

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TITLE: Balanced Sampling Design: An Improvement Over the
Classical Stratified Sampling Design
SPEAKER: Yan Liu
Dept of Statistics
The George Washington University
DATE: November 12, 1998
LOCATION: 323 Funger Hall
TIME: 10:00 a.m.

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Design-based inference has had a dominant role in survey sampling of
finite population for many years. It faces, though, the criticism that an
unlucky sample can result in misleading conclusions. To avoid this, some
survey statisticians employ model-based or model-assisted approaches.
Another solution, is to work at the design stage to identify a restricted
subset of all possible samples and then randomly select a sample from that
subset. These so called preferred samples, are such that samples which
are not desirable, do not get selected.

This dissertation will develop some operationally simple sampling schemes
that confine random selections to preferred samples. The proposed median
balanced sampling, design is the modification of a conventional stratified
sampling design to a preferred one. It begins by altering the choice of
stratum boundaries, then balances the selections among strata by employing
the strata medians. The balancing creates a dependency in the selections
across strata that reduces the overall variance while the unconditional
selection probability of each unit remains unchanged. Given this setup, it
is proved that the variance of the estimator of the population mean in a
median balanced sampling design is more stable than with a conventional
approach (which selects units in each stratum independently). Both
sampling with and without replacement are covered and balancing on the
mean instead of the median is also considered. The efficiency gain of
ratio and regression estimation due to the median balanced sampling design
is discussed as well. Some large sample results are derived and finally a
simulation is done of median balancing under a plausible application.
In many settings, the median balanced design can be seen as a great
improvement over conventional stratified sampling.
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TITLE: Probabilities, Causes, and Toxic Torts
SPEAKER: Mark Parascandola
Department of Clinical Bioethics
National Institutes of Health
DATE: December 4, 1998
LOCATION: 221 Funger Hall
TIME: 11:00 a.m.

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In litigation regarding mass toxic exposure and causation of chronic
disease it is usually impossible to identify a single factor as the
exclusive cause of any individual's disease. Hence, the "problem of the
indeterminate plaintiff." In these cases plaintiffs rely on epidemiologic
evidence to show a probability that their disease was caused by the toxic
exposure. The law has allowed that such evidence is acceptable in many
instances, but the plaintiff typically must demonstrate that the exposure
more than doubled the risk of disease to prove causation. However, this
requirement and the "probability of causation" formula used make numerous
problematic statistical and biological assumptions. Additionally, this
approach fails to fulfill the policy goals it is intended to protect, and
it has important, and often undesirable, consequences for tort law and the
regulatory system.
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TITLE: STATISTICAL REALITIES FOR FINANCIAL TIME SERIES
SPEAKER: C. C. Heyde
Columbia University and Australian National University
DATE: December 11, 1998
LOCATION: TBA
TIME: TBA

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Much confusion has surrounded the statistical evidence related to the
issues of heavy tails, volatility and long range dependence in financial
time series. The talk will focus on the log returns process in risky
asset modelling and in that setting the major sources of confusion,
especially the sensitivity of tail estimation procedures and some long
range dependence parameter estimators to likely departures from their
standard operating conditions will be discussed. Recent evidence on
leptokurtic tails, heteroscedastic conditional variances, and the presence
of a heavy tailed subordinated distribution exhibiting long range
dependence will be discussed. The simplest variant on geometric Brownian
motion possessing the features required by the statistical evidence will
be described.

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

or 202-994-6359.