Francisco José A. Cysneiros

Pelagic microplastics around an archipelago of the Equatorial Atlantic

Plastic marine debris is presently widely recognised as an important environmental pollutant. Such debris is reported in every habitat of the oceans, from urban tourist beaches to remote islands and from the ocean surface to submarine canyons, and is found buried and deposited on sandy and cobble beaches. Plastic marine debris varies from micrometres to several metres in length and is potentially ingested by animals of every level of the marine food web. Here, we show that synthetic polymers are present in subsurface plankton samples around Saint Peter and Saint Paul Archipelago in the Equatorial Atlantic Ocean. To explain the distribution of microplastics around the Archipelago, we proposed a generalised linear model (GLM) that suggests the existence of an outward gradient of mean plastic-particle densities. Plastic items can be autochthonous or transported over large oceanic distances. One probable source is the small but persistent fishing fleet using the area.

Birnbaum–Saunders statistical modelling: a new approach

Modelling based on the Birnbaum–Saunders distribution has received considerable attention in recent years. In this article, we introduce a new approach for Birnbaum–Saunders regression models, which allows us to analyze data in their original scale and to model non-constant variance. In addition, we propose four types of residuals for these models and conduct a simulation study to establish which of them has a better performance. Moreover, we develop methods of local influence by calculating the normal curvatures under different perturbation schemes. Finally, we perform a statistical analysis with real data by using the approach proposed in the article. This analysis shows the potentiality of our proposal.

Restricted methods in symmetrical linear regression models

In this paper we discuss the problem of testing equality and inequality constraints in symmetrical linear regression models. This class of models includes all symmetric continuous distributions, such as normal, Student-t, Pearson VII, power exponential and logistic, among others. It is commonly used for the analysis of data containing influential or outlying observations with responses supposedly normal. Iterative processes for evaluating the parameters under equality and inequality constraints are presented. The asymptotic null distribution of three asymptotically equivalent one-sided tests is showed to be invariant with the symmetrical error. A sensitivity study to investigate the robustness of the maximum likelihood estimates from some symmetrical models against high leverage and influential observations is presented. An illustrative example with presence of influential observations on the decisions from the statistical tests of different symmetrical models is given. The robustness aspects of such models are also discussed.

A robust method for linear regression of symbolic interval data

This paper introduces a new linear regression method for interval valued-data. The method is based on the symmetrical linear regression methodology such that the prediction of the lower and upper bounds of the interval value of the dependent variable is not damaged by the presence of interval-valued data outliers. The method considers mid-points and ranges of the interval values assumed by the variables in the learning set. The prediction of the boundaries of an interval is accomplished through a combination of predictions from mid-point and range of the interval values. The evaluation of the method is based on the average behavior of a pooled root mean-square error. Experiments with real and simulated symbolic interval data sets demonstrate the usefulness of this symbolic symmetrical linear regression method.

Assessment of diagnostic procedures in symmetrical nonlinear regression models

The aim of this paper is to derive diagnostic procedures based on case-deletion model for symmetrical nonlinear regression models, which complements Galea et al. (2005) that developed local influence diagnostics under some perturbation schemes. This class of models includes all symmetric continuous distributions for errors covering both light- and heavy-tailed distributions such as Student-t, logistic-I and -II, power exponential, generalized Student-t, generalized logistic and contaminated normal, among others. Thus, these models can be checked for robustness to outliers in the response variable and diagnostic methods may be a useful tool for an appropriate choice. First, an iterative process for the parameter estimation as well as some inferential results are presented. Besides, we present the results of a simulation study in which the characteristics of heavy-tailed models are evaluated in the presence of outliers. Then, we derive some diagnostic measures such as Cook distance, W-K statistic, one-step approach and likelihood displacement, generalizing results obtained for normal nonlinear regression models. Also, we present simulation studies that illustrate the behavior of diagnostic measures proposed. Finally, we consider two real data sets previously analyzed under normal nonlinear regression models. The diagnostic analysis indicates that a Student-t nonlinear regression model seems to fit the data better than the normal nonlinear regression model as well as other symmetrical nonlinear models in the sense of robustness against extreme observations.

Diagnostics in multivariate generalized Birnbaum-Saunders regression models

ABSTRACT Birnbaum–Saunders (BS) models are receiving considerable attention in the literature. Multivariate regression models are a useful tool of the multivariate analysis, which takes into account the correlation between variables. Diagnostic analysis is an important aspect to be considered in the statistical modeling. In this paper, we formulate multivariate generalized BS regression models and carry out a diagnostic analysis for these models. We consider the Mahalanobis distance as a global influence measure to detect multivariate outliers and use it for evaluating the adequacy of the distributional assumption. We also consider the local influence approach and study how a perturbation may impact on the estimation of model parameters. We implement the obtained results in the R software, which are illustrated with real-world multivariate data to show their potential applications.

Robust regression with application to symbolic interval data

This paper presents a robust regression model that deals with cases that have interval-valued outliers in the input data set. Each interval of the input data is represented by its range and midpoint and the fitting to interval-valued data is not sensible in the presence of midpoint and/or range outliers on the interval response. The predictions of the lower and upper bounds of new intervals are performed and simulation studies are carried out to validate these predictions. Two applications with real-life interval data sets are considered. The prediction quality is assessed by a mean magnitude of relative error calculated from a test data set.

Logistic regression-based pattern classifiers for symbolic interval data

This paper introduces different pattern classifiers for interval data based on the logistic regression methodology. Four approaches are considered. These approaches differ according to the way of representing the intervals. The first classifier considers that each interval is represented by the centres of the intervals and performs a classic logistic regression on the centers of the intervals. The second one assumes each interval as a pair of quantitative variables and performs a conjoint classic logistic regression on these variables. The third one considers that each interval is represented by its vertices and a classic logistic regression on the vertices of the intervals is applied. The last one assumes each interval as a pair of quantitative variables, performs two separate classic logistic regressions on these variables and combines the results in some appropriate way. Experiments with synthetic data sets and an application with a real interval data set demonstrate the usefulness of these classifiers.

Diagnostic procedures in Birnbaum-Saunders nonlinear regression models

This paper proposes a general definition of residuals for Birnbaum-Saunders nonlinear regression models by studying their statistical properties analytically and using Monte Carlo experiments. Also, some diagnostic procedures are derived based on case-deletion and mean-shift outlier models such as one-step approximation, likelihood displacement, generalized Cooks distance, outlier tests and some measures for identifying influential observations on partial F-test. A test for homogeneity of shape parameter is also developed. Residuals and influence diagnostic tools are illustrated by means of an example that allows us to relate the response variable lifetime of a metal piece and the explanatory variable work per cycle. Three models were compared to fit the dataset, two of them with nonlinear systematic components.

A Multivariate Log-Linear Model for Birnbaum-Saunders Distributions

Univariate Birnbaum-Saunders models have been widely applied to fatigue studies. Calculation of fatigue life is of great importance in determining the reliability of materials. We propose and derive new multivariate generalized Birnbaum-Saunders regression models. We use the maximum likelihood method and the EM algorithm to estimate their parameters. We carry out a simulation study to evaluate the performance of the corresponding maximum likelihood estimators. We illustrate the new models with real-world multivariate fatigue data.