arXiv subjects

Miguel de Carvalho

Publications and source records attributed to Miguel de Carvalho.

26 records · Page 2Linked to original sources

arXiv2020

Modeling Interval Trendlines: Symbolic Singular Spectrum Analysis for Interval Time Series

In this article we propose an extension of singular spectrum analysis for interval-valued time series. The proposed methods can be used to decompose and forecast the dynamics governing a set-valued stochastic process. The resulting components on which the interval time series is decomposed can be understood as interval trendlines, cycles, or noise. Forecasting can be conducted through a linear recurrent method, and we devised generalizations of the decomposition method for the multivariate setting. The performance of the proposed methods is showcased in a simulation study. We apply the proposed methods so to track the dynamics governing the Argentina Stock Market (MERVAL) in real time, in a case study that covers the most recent period of turbulence that led to discussions of the government of Argentina with the International Monetary Fund.

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arXiv2020

Robust and flexible inference for the covariate-specific ROC curve

Diagnostic tests are of critical importance in health care and medical research. Motivated by the impact that atypical and outlying test outcomes might have on the assessment of the discriminatory ability of a diagnostic test, we develop a flexible and robust model for conducting inference about the covariate-specific receiver operating characteristic (ROC) curve that safeguards against outlying test results while also accommodating for possible nonlinear effects of the covariates. Specifically, we postulate a location-scale additive regression model for the test outcomes in both the diseased and nondiseased populations, combining additive cubic B-splines and M-estimation for the regression function, while the residuals are estimated via a weighted empirical distribution function. The results of the simulation study show that our approach successfully recovers the true covariate-specific ROC curve and corresponding area under the curve on a variety of conceivable test outcomes contamination scenarios. Our method is applied to a dataset derived from a prostate cancer study where we seek to assess the ability of the Prostate Health Index to discriminate between men with and without Gleason 7 or above prostate cancer, and if and how such discriminatory capacity changes with age.

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arXiv2018

On the geometry of Bayesian inference

We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the simple observation that the marginal likelihood can be regarded as an inner product between the prior and the likelihood. A key concept in our geometry is that of compatibility, a measure which is based on the same construction principles as Pearson correlation, but which can be used to assess how much the prior agrees with the likelihood, to gauge the sensitivity of the posterior to the prior, and to quantify the coherency of the opinions of two experts. Estimators for all the quantities involved in our geometric setup are discussed, which can be directly computed from the posterior simulation output. Some examples are used to illustrate our methods, including data related to on-the-job drug usage, midge wing length, and prostate cancer.

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arXiv2018

Bayesian Bootstrap Inference for the ROC Surface

Accurate diagnosis of disease is of great importance in clinical practice and medical research. The receiver operating characteristic (ROC) surface is a popular tool for evaluating the discriminatory ability of continuous diagnostic test outcomes when there exist three ordered disease classes (e.g., no disease, mild disease, advanced disease). We propose the Bayesian bootstrap, a fully nonparametric method, for conducting inference about the ROC surface and its functionals, such as the volume under the surface. The proposed method is based on a simple, yet interesting, representation of the ROC surface in terms of placement variables. Results from a simulation study demonstrate the ability of our method to successfully recover the true ROC surface and to produce valid inferences in a variety of complex scenarios. An application to data from the Trail Making Test to assess cognitive impairment in Parkinson's disease patients is provided.

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arXiv2017

Affinity-based measures of medical diagnostic test accuracy

We propose new summary measures of diagnostic test accuracy which can be used as companions to existing diagnostic accuracy measures. Conceptually, our summary measures are tantamount to the so-called Hellinger affinity and we show that they can be regarded as measures of agreement constructed from similar geometrical principles as Pearson correlation. A covariate-specific version of our summary index is developed, which can be used to assess the discrimination performance of a diagnostic test, conditionally on the value of a predictor. Nonparametric Bayes estimators for the proposed indexes are devised, theoretical properties of the corresponding priors are derived, and the performance of our methods is assessed through a simulation study. Data from a prostate cancer diagnosis study are used to illustrate our methods.

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arXiv2017

Regression Type Models for Extremal Dependence

We propose a vector generalized additive modeling framework for taking into account the effect of covariates on angular density functions in a multivariate extreme value context. The proposed methods are tailored for settings where the dependence between extreme values may change according to covariates. We devise a maximum penalized log-likelihood estimator, discuss details of the estimation procedure, and derive its consistency and asymptotic normality. The simulation study suggests that the proposed methods perform well in a wealth of simulation scenarios by accurately recovering the true covariate-adjusted angular density. Our empirical analysis reveals relevant dynamics of the dependence between extreme air temperatures in two alpine resorts during the winter season. Supplementary materials for this article are available online.

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arXiv2017

Time-Varying Extreme Value Dependence with Application to Leading European Stock Markets

Extremal dependence between international stock markets is of particular interest in today's global financial landscape. However, previous studies have shown this dependence is not necessarily stationary over time. We concern ourselves with modeling extreme value dependence when that dependence is changing over time, or other suitable covariate. Working within a framework of asymptotic dependence, we introduce a regression model for the angular density of a bivariate extreme value distribution that allows us to assess how extremal dependence evolves over a covariate. We apply the proposed model to assess the dynamics governing extremal dependence of some leading European stock markets over the last three decades, and find evidence of an increase in extremal dependence over recent years.

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arXiv2012

A Euclidean likelihood estimator for bivariate tail dependence

The spectral measure plays a key role in the statistical modeling of multivariate extremes. Estimation of the spectral measure is a complex issue, given the need to obey a certain moment condition. We propose a Euclidean likelihood-based estimator for the spectral measure which is simple and explicitly defined, with its expression being free of Lagrange multipliers. Our estimator is shown to have the same limit distribution as the maximum empirical likelihood estimator of J. H. J. Einmahl and J. Segers, Annals of Statistics 37(5B), 2953--2989 (2009). Numerical experiments suggest an overall good performance and identical behavior to the maximum empirical likelihood estimator. We illustrate the method in an extreme temperature data analysis.

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