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EDSEL E. PENA, PhD
Global
Validation of Linear Model Assumptions (with E. Slate). To
appear in the Journal of the American Statistical
Association, 2005.
No abstract available.
Dynamic Modelling in Reliability and
Survival Analysis (with E. Slate). To appear in the
Mathematical and Statistical Methods in Reliability, 2005.
No abstract available.
Modelling treatment effects after
cancer relapses, with applications to recurrences in
indolent non-Hodgkin's lymphomas (with J. Gonzalez and E.
Slate). To appear in Statistics in Medicine, 2005.
No abstract available.
Joint Analysis of Longitudinal and
Recurrent Event Outcomes (with E. Slate). Fourth
International Conference on Mathematical Methods in
Reliability: Methodology and Practice. In CD-ROM, Santa Fe,
NM, 4 pages.
No abstract available.
Dynamic Models in Reliability and
Survival Analysis (with E. Slate). Fourth International
Conference on Mathematical Methods in Reliability:
Methodology and Practice. In CD-ROM, Santa Fe, NM, 4 pages.
No abstract available.
Nonparametric Methods in Reliability
(with M. Hollander), Statistical Science, 2004, 19, 644{651.
No abstract available
Estimating Load-Sharing Properties in
a Dynamic Reliability System (with P. Kvam). Journal of the
American Statistical Association, 2005, 100, 262{272.
An estimator for the load-share
parameters in an equal load-share model is derived based on
observing k-component parallel systems of identical
components that have a continuous distribution function F ()
and failure rate r (). In an equal load-share model, after
the first of k components fails, failure rates for the
remaining components change from r (t) to 1r (t), then to 2r
(t) after the next failure, and so on. On the basis of
observations on n independent and identical systems, a
semiparametric estimator of the component baseline
cumulative hazard function R = -log(1 - F) is presented, and
its asymptotic limit process is established to be a Gaussian
process. The effect of estimation of the load-share
parameters is considered in the derivation of the limiting
process. Potential applications can be found in diverse
areas, including materials testing, software reliability,
and power plant safety assessment.
Variance Estimation in a Model with
Gaussian Submodels (with V. Dukic). Journal of the American
Statistical Association, 2005, 100, 296{309.
This article considers the problem of
estimating the dispersion parameter in a Gaussian model that
is intermediate between a model where the mean parameter is
fully known (fixed) and a model where the mean parameter is
completely unknown. One of the goals is to understand the
implications of the two-step process of first selecting a
model among a finite number of submodels, then estimating a
parameter of interest after the model selection, but using
the same sample data. The estimators are classified into
global, two-step, and weighted estimators. Whereas the
global-type estimators ignore the model space structure, the
two-step estimators explore the structure adaptively and can
be related to pretest estimators, and the weighted
estimators are motivated by the Bayesian approach. Their
performances are compared theoretically and through
simulations using their risk functions based on a
scale-invariant quadratic loss function. It is shown that in
the variance estimation problem, efficiency gains arise by
exploiting the submodel structure through the use of
two-step and weighted estimators, especially when the number
of competing submodels is few, but that this advantage may
deteriorate or be lost altogether for some two-step
estimators as the number of submodels increases or the
distance between them decreases. Furthermore, it is
demonstrated that weighted estimators, arising from properly
chosen priors, outperform two-step estimators when there are
many competing submodels or when the submodels are close to
each other, whereas two-step estimators are preferred when
the submodels are highly distinguishable. The results have
implications for model averaging and model selection issues.
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