A. Alexandre (Alex) Trindade
Personal Information
Teaching
Research
List of statistical methodology research, arranged in approximate
chronological order:
- 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.
- 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 seminal work was funded by the National Security
Agency.) 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.
- 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.
- Tail Risk Modeling. In Barnard, Pearce, & Trindade (2018), The Annals of Operations Research, we have unveiled interesting asymptotic efficiency calculations comparing expected shortfall with value-at-risk, both in light-tailed and heavy-tailed settings. In Belhad, Lauria, & Trindade (2022), Journal of Risk, we introduced new nonparametric estimates of systemic risk as measured by conditional value-at-risk, the so called CoVaR.
- Nonparametric inference. With Igor Volobouev we are
tackling signal detection and inverse problems motivated by high
energy physics (HEP) data. Early work resulted in a novel method of
density estimation based on local orthogonal polynomials:
Dassanayake, Volobouev, & Trindade (2017), Journal of
Nonparametric Statistics. In Volobouev, & Trindade
(2018), JINST, and Wellalage, Volobouev, & Trindade
(2023), Test, we have proposed high-order approximations for
improving inference in a mixture model under a false discovery rate
control paradigm. In Guglielmini, Volobouev & Trindade
(2025), Statistics and Computing, we have proposed a method
to measure the effective number of parameters in kernel density estimation.
Books
Recent Talks
Ph.D. Dissertation (1 MB)
Collaborative Research and Consulting
List of significant collaborative research and consulting projects.
- Starting in 2020, I have been involved in fertility research with
Stephen Usuala (MD, PhD), Texas Tech University Health Sciences
Center, Amarillo. The main idea is to be able to accurately predict
the menstrual cycle phase based on easy to measure variables.
- Starting in 2017, I have a collaboration with Ahmed Alzahabi (Petroleum Engineering Dept., University of Texas of the Permian Basin), on various supervised and unsupervised machine learning projects connected with predicting and optimizing hydrocarbons.
- 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.
- 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.
- 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.
Datasets and Software
Other Links
Amusements...