A. Alexandre (Alex) Trindade
My statistical methodology research encompasses the following primary areas of focus.
- Saddlepoint-Based Bootstrap (SPBB). Together with Rob Paige, we
have devised a method to make approximate (but accurate) inference for a (scalar) parameter
where the distribution of the estimator is intractable. If a profile estimating
equation can be derived that is a quadratic form in normal random variables (QEE), a
saddlepoint approximation for the distribution of the QEE can be
obtained. Under monotonicity of the QEE in the parameter, the saddlepoint approximation of the
QEE can be related to that of the estimator, whence p-values can be calculated
or confidence intervals constructed by pivoting the distribution function. The
main paper here is: Paige, Trindade, & Fernando (2009), Scandinavian
Journal of Statistics. This work has been funded by the National Security
- Time Series Modeling. My dissertation topic was on estimators for
multivariate autoregressive (VAR) models. Together with Peter Brockwell,
Richard Davis, and Rainer Dahlhaus, we devised a series of Burg-type estimators
for subset VARs. The
main paper here is: Brockwell, Dahlhaus, & Trindade (2005), Statistica
Sinica. The SPBB approach is applicable here, and one thrust of my
current work is in this direction. Other directions and loose ends currently include
inference under asymmetric Laplace and other skewed distributions, multivariate volatility
modeling, state-space models, and generalized autocorrelation to discriminate between independent
and serially uncorrelated sequences. This latter idea is tied to our paper on
all-pass models, which in the non-Gaussian case generate serially uncorrelated
but dependent sequences: Breidt, Davis, & Trindade (2001), The Annals of Statistics.
- Longitudinal/Spatial Modeling. An application of SPBB in spatial regression models led to the paper: Jeganathan, Paige, & Trindade (2015), Spatial Statistics. In longitudinal modeling, we have extended the state-space model to handle missing values in responses and covariates: Naranjo, Trindade, & Casella (2013), Journal of the American Statistical Association. Collaborations struck during this work led to the monograph: Casals, Garcia-Hiernaux, Jerez, Sotoca, & Trindade (CRC Press, 2016), State-Space Methods for Time Series Analysis: Theory, Applications and Software.
- Miscellaneous & Recent. I continue with sporadic risk modeling work, in a recent collaboration we have unveiled interesting asymptotic efficiency calculations comparing expected shortfall with value-at-risk, both in light-tailed and heavy-tailed settings: Barnard, Pearce, & Trindade (2017+), The Annals of Operations Research. Recent novel applications of SPBB with Rob Paige and our students are resulting in methods for reconstructing survival functions under various censoring regimes, by combining empirical masses from NPMLE with parametric tails.
With Igor Volobouev we are tackling signal detection and inverse problems arising from particle physics data. Currently this has resulted in a novel method of density estimation based on local orthogonal polynomials: Dassanayake, Volobouev, & Trindade (2017+), Journal of Nonparametric Statistics). Most recently we have proposed Edgeworth expansions for improving inference in a mixture model in the context of searching for rare signals under a false discovery rate control paradigm.
Recent Technical Reports
- Volobouev, I., and Trindade, A.A., "Improved Inference for the Signal Significance".
- Jeganathan, P., Randrianampy, N.V., Paige, R.L. and Trindade, A.A.,
``An Empirical Saddlepoint Approximation Based Method for Smoothing Survival Functions Under Right Censoring''.
Ph.D. Dissertation (1 MB)
Collaborative Research and Consulting
I have been involved in a number of collaborative research and statistical consulting projects.
- In 2012 I worked on the phylogenetic analysis of certain bacterial genomes with the Biological Sciences Dept., Texas Tech University. This work resulted in 2
papers with Chadha as senior author (see my CV).
- In 2006-2007 I worked with researchers in nuclear and radiological
engineering at the University of Florida to develop statistical models for predicting optimal doses in
patients undergoing radiation treatment. This work resulted in 3
papers with Bolch as senior author (see my CV).
- In 2005 I was contracted by Encision, Inc., for a reliability study on medical
devices. This work resulted in 2 unpublished reports.
- In 2004-2005 I was subcontracted by American Optimal Decisions for a
materials science research project funded by The Institute for Defence
Analysis that aimed to develop new steels. This work resulted in 3 papers
with Uryasev and Macheret as senior authors (see my CV).
- In 2003-2004 I was the primary statistical consultant on a reliability project
with The Boeing Company funded by DARPA. This work resulted in 2
unpublished reports and 3 papers with Uryasev as senior author (see my CV).
Datasets and Software
Finance-Related Links and Software
- Jurgen Doornik's object oriented statistical system Ox, and the companion Ox GARCH package.
- Rmetrics, a
collection of R packages for financial engineering and computational finance.
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