Diagnostic Analytics for an Autoregressive Model under the Skew-Normal Distribution

Robust autoregressive modeling and its diagnostic analytics with a COVID-19 related application

Autoregressive models in time series are useful in various areas. In this article, we propose a skew-t autoregressive model. We estimate its parameters using the expectation-maximization (EM) method and develop the influence methodology based on local perturbations for its validation. We obtain the normal curvatures for four perturbation strategies to identify influential observations, and then to assess their performance through Monte Carlo simulations. An example of financial data analysis is presented to study daily log-returns for Brent crude futures and investigate possible impact by the COVID-19 pandemic.

Bayesian Influence Analysis of the Skew-Normal Spatial Autoregression Models

In spatial data analysis, outliers or influential observations have a considerable influence on statistical inference. This paper develops Bayesian influence analysis, including the local influence approach and case influence measures in skew-normal spatial autoregression models (SSARMs). The Bayesian local influence method is proposed to evaluate the impact of small perturbations in data, the distribution of sampling and prior. To measure the extent of different perturbations in SSARMs, the Bayes factor, the ϕ-divergence and the posterior mean distance are established. A Bayesian case influence measure is presented to examine the influence points in SSARMs. The potential influence points in the models are identified by Cook’s posterior mean distance and Cook’s posterior mode distance ϕ-divergence. The Bayesian influence analysis formulation of spatial data is given. Simulation studies and examples verify the effectiveness of the presented methodologies.

A Type I Generalized Logistic Distribution: Solving Its Estimation Problems with a Bayesian Approach and Numerical Applications Based on Simulated and Engineering Data

The family of logistic type distributions has been widely studied and applied in the literature. However, certain estimation problems exist in some members of this family. Particularly, the three-parameter type I generalized logistic distribution presents these problems, where the parameter space must be restricted for the existence of their maximum likelihood estimators. In this paper, motivated by the complexities that arise in the inference under the likelihood approach utilizing this distribution, we propose a Bayesian approach to solve these problems. A simulation study is carried out to assess the performance of some posterior distributional characteristics, such as the mean, using Monte Carlo Markov chain methods. To illustrate the potentiality of the Bayesian estimation in the three-parameter type I generalized logistic distribution, we apply the proposed method to real-world data related to the copper metallurgical engineering area.

Data-Influence Analytics in Predictive Models Applied to Asthma Disease

Asthma is one of the most common chronic diseases around the world and represents a serious problem in human health. Predictive models have become important in medical sciences because they provide valuable information for data-driven decision-making. In this work, a methodology of data-influence analytics based on mixed-effects logistic regression models is proposed for detecting potentially influential observations which can affect the quality of these models. Global and local influence diagnostic techniques are used simultaneously in this detection, which are often used separately. In addition, predictive performance measures are considered for this analytics. A study with children and adolescent asthma real data, collected from a public hospital of São Paulo, Brazil, is conducted to illustrate the proposed methodology. The results show that the influence diagnostic methodology is helpful for obtaining an accurate predictive model that provides scientific evidence when data-driven medical decision-making.

A Family of Skew-Normal Distributions for Modeling Proportions and Rates with Zeros/Ones Excess

In this paper, we consider skew-normal distributions for constructing new a distribution which allows us to model proportions and rates with zero/one inflation as an alternative to the inflated beta distributions. The new distribution is a mixture between a Bernoulli distribution for explaining the zero/one excess and a censored skew-normal distribution for the continuous variable. The maximum likelihood method is used for parameter estimation. Observed and expected Fisher information matrices are derived to conduct likelihood-based inference in this new type skew-normal distribution. Given the flexibility of the new distributions, we are able to show, in real data scenarios, the good performance of our proposal.

Cokriging Prediction Using as Secondary Variable a Functional Random Field with Application in Environmental Pollution

Cokriging is a geostatistical technique that is used for spatial prediction when realizations of a random field are available. If a secondary variable is cross-correlated with the primary variable, both variables may be employed for prediction by means of cokriging. In this work, we propose a predictive model that is based on cokriging when the secondary variable is functional. As in the ordinary cokriging, a co-regionalized linear model is needed in order to estimate the corresponding auto-correlations and cross-correlations. The proposed model is utilized for predicting the environmental pollution of particulate matter when considering wind speed curves as functional secondary variable.

Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.

Approximating the Distribution of the Product of Two Normally Distributed Random Variables

The distribution of the product of two normally distributed random variables has been an open problem from the early years in the XXth century. First approaches tried to determinate the mathematical and statistical properties of the distribution of such a product using different types of functions. Recently, an improvement in computational techniques has performed new approaches for calculating related integrals by using numerical integration. Another approach is to adopt any other distribution to approximate the probability density function of this product. The skew-normal distribution is a generalization of the normal distribution which considers skewness making it flexible. In this work, we approximate the distribution of the product of two normally distributed random variables using a type of skew-normal distribution. The influence of the parameters of the two normal distributions on the approximation is explored. When one of the normally distributed variables has an inverse coefficient of variation greater than one, our approximation performs better than when both normally distributed variables have inverse coefficients of variation less than one. A graphical analysis visually shows the superiority of our approach in relation to other approaches proposed in the literature on the topic.

Birnbaum-Saunders Quantile Regression Models with Application to Spatial Data

In the present paper, a novel spatial quantile regression model based on the Birnbaum–Saunders distribution is formulated. This distribution has been widely studied and applied in many fields. To formulate such a spatial model, a parameterization of the multivariate Birnbaum–Saunders distribution, where one of its parameters is associated with the quantile of the respective marginal distribution, is established. The model parameters are estimated by the maximum likelihood method. Finally, a data set is applied for illustrating the formulated model.