We extend our methods to the situations when the disease has multiple
categories, when one has a set of mutually associated exposures, or when the
exposures are measured with errors.

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We consider simultaneous estimation of finite population means for several
strata based on two different model structures and assumptions. In each
consideration,a model-based approach is taken, where the covariates in the
super-population model are subject to measurement errors. In the
first set-up, EB estimators of the strata means are developed
and an asymptotic expression of the Mean Square Error of the vector of EB
estimators is attained. In the second set-up, we consider developing both EB
and HB estimators of the strata means. In both cases, findings
are supported by appropriate data analyses and are further validated by
simulation studies.

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(This is joint work with Christian Robert, Universite Paris
Dauphine.)

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This is joint work with U. Amato (CNR, Naples, Italy) and
A. Antoniadis (Laboratoire IMAG-LMC, University Joseph Fourier, France).

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Previous analyses of warping have typically not been based on a model where individual observed curves are viewed as realizations of a stochastic process. We propose a functional convex synchronization model, under the premise that each observed curve is the realization of a stochastic process. Monotonicity constraints on time evolution provide the motivation for a functional convex calculus with the goal of obtaining sample statistics such as a functional mean. Observed random functions in warped time space are represented by a bivariate random function in synchronized time space, consisting of a stochastic monotone time transformation function and an unrestricted random amplitude function. This leads to the definition of a functional convex average or "longitudinal average", which is in contrast to the conventional "cross-sectional" average. We derive a functional limit theorem and asymptotic confidence intervals for functional convex means. The results are illustrated with a novel time warping transformation. The methods are applied to simulated data and the Berkeley growth data. This nonparametric time-synchronized algorithm is also combined with an iterative mean updating technique to find an overall representation that corresponds to a mode of a sample of gene expression profiles, viewed as a random sample in function space.

This talk is based on joint works with Dr. Hans-Georg Müller.

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Based on a recent paper by Kong, McCullagh, Meng, Nicolae, and Tan
(Journal of The Royal Statistical Society, 2003, 585-618), this talk
demonstrates that a satisfactory answer to such questions not only satisfies
our philosophical curiosity, but more importantly
it can lead to Monte Carlo estimators with efficiency that are generally
unaware of. In particularly we give a practical example where the new
Monte Carlo estimator converges at the super fast 1/n rate instead of the
usual 1/sqrt(n) rate, where n is the size of the simulation data.

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(joint work with Subhasis Ghosal, NCSU)

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We also argue that because there is no realistic situation that corresponds to
the case of conditioning on both margins of a contingency table, the proper
analysis of an *a* × *b* contingency table should only
condition on either the table total or on only one of the margins. The
posterior probabilities from the intrinsic priors provide reasonable answers
in these cases. Examples using simulated and real data are given.

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Suppose you, as a medical journal reviewer, read a report of a randomized
clinical trial that fails to mention any sequential monitoring plan. Can you
ask the "What if" question without obtaining the actual data? Surprisingly,
in many instances, the answer is yes. If the trial information accrues as
approximate Brownian Motion, then the joint predictive distribution of any
collection of effect size estimates at times before the final analysis depends
only upon the effect size estimate at the final analysis. Hence, you can
superimpose a hypothetical group sequential design upon the non-sequential
design. As a side benefit of this research, reference designs, with optimal
or near optimal expected sample sizes relative to single stage designs, are
presented so that as a reviewer you would simply consult a table to assess the
predictive probabilities for each stopping time and the conditional mean
sample size. In addition, you can superimpose your own group sequential design
upon an actual group sequential design to second guess what you think was a
poor choice of stopping boundaries. In this case, you need the Z-scores (or
single degree of freedom chi-squares) at each interim look. This new
capability should alter the mindset of those designing clinical trials. Since
journal editors and the public can subject the trial to close scrutiny after
the fact, trial designers will be more motivated to making their designs as
efficient as possible. We shall present two actual examples that were heavily
criticized for staying open too long. In one, it is probable that
participants were not properly protected, and a report of critically important
public health benefit was withheld unreasonably from the public. In the
other, the criticism seems to have been unfounded.

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