On beta regression residuals

We propose two new residuals for the class of beta regression models, and numerically evaluate their behaviour relative to the residuals proposed by Ferrari and Cribari-Neto. Monte Carlo simulation results and empirical applications using real and simulated data are provided. The results favour one of the residuals we propose.

Missing data mechanisms and their implications on the analysis of categorical data

We review some issues related to the implications of different missing data mechanisms on statistical inference for contingency tables and consider simulation studies to compare the results obtained under such models to those where the units with missing data are disregarded. We confirm that although, in general, analyses under the correct missing at random and missing completely at random models are more efficient even for small sample sizes, there are exceptions where they may not improve the results obtained by ignoring the partially classified data. We show that under the missing not at random (MNAR) model, estimates on the boundary of the parameter space as well as lack of identifiability of the parameters of saturated models may be associated with undesirable asymptotic properties of maximum likelihood estimators and likelihood ratio tests; even in standard cases the bias of the estimators may be low only for very large samples. We also show that the probability of a boundary solution obtained under the correct MNAR model may be large even for large samples and that, consequently, we may not always conclude that a MNAR model is misspecified because the estimate is on the boundary of the parameter space.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

Multivariate measurement error models based on scale mixtures of the skew-normal distribution

Scale mixtures of the skew-normal (SMSN) distribution is a class of asymmetric thick-tailed distributions that includes the skew-normal (SN) distribution as a special case. The main advantage of these classes of distributions is that they are easy to simulate and have a nice hierarchical representation facilitating easy implementation of the expectation-maximization algorithm for the maximum-likelihood estimation. In this paper, we assume an SMSN distribution for the unobserved value of the covariates and a symmetric scale mixtures of the normal distribution for the error term of the model. This provides a robust alternative to parameter estimation in multivariate measurement error models. Specific distributions examined include univariate and multivariate versions of the SN, skew-t, skew-slash and skew-contaminated normal distributions. The results and methods are applied to a real data set.

Diagnostic tools in beta regression with varying dispersion

We consider the issue of performing residual and local influence analyses in beta regression models with varying dispersion, which are useful for modelling random variables that assume values in the standard unit interval. In such models, both the mean and the dispersion depend upon independent variables. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. An application using real data is presented and discussed.

Influence diagnostics for linear models with first-order autoregressive elliptical errors

We introduce in this paper the class of linear models with first-order autoregressive elliptical errors. The score functions and the Fisher information matrices are derived for the parameters of interest and an iterative process is proposed for the parameter estimation. Some robustness aspects of the maximum likelihood estimates are discussed. The normal curvatures of local influence are also derived for some usual perturbation schemes whereas diagnostic graphics to assess the sensitivity of the maximum likelihood estimates are proposed. The methodology is applied to analyse the daily log excess return on the Microsoft whose empirical distributions appear to have AR(1) and heavy-tailed errors. (C) 2008 Elsevier B.V. All rights reserved.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

Covariance matrix formula for Birnbaum-Saunders regression models

The Birnbaum-Saunders regression model is commonly used in reliability studies. We derive a simple matrix formula for second-order covariances of maximum-likelihood estimators in this class of models. The formula is quite suitable for computer implementation, since it involves only simple operations on matrices and vectors. Some simulation results show that the second-order covariances can be quite pronounced in small to moderate sample sizes. We also present empirical applications.

Bias-corrected estimators for dispersion models with dispersion covariates

In this paper we discuss bias-corrected estimators for the regression and the dispersion parameters in an extended class of dispersion models (Jorgensen, 1997b). This class extends the regular dispersion models by letting the dispersion parameter vary throughout the observations, and contains the dispersion models as particular case. General formulae for the O(n(-1)) bias are obtained explicitly in dispersion models with dispersion covariates, which generalize previous results obtained by Botter and Cordeiro (1998), Cordeiro and McCullagh (1991), Cordeiro and Vasconcellos (1999), and Paula (1992). The practical use of the formulae is that we can derive closed-form expressions for the O(n(-1)) biases of the maximum likelihood estimators of the regression and dispersion parameters when the information matrix has a closed-form. Various expressions for the O(n(-1)) biases are given for special models. The formulae have advantages for numerical purposes because they require only a supplementary weighted linear regression. We also compare these bias-corrected estimators with two different estimators which are also bias-free to order O(n(-1)) that are based on bootstrap methods. These estimators are compared by simulation. (C) 2011 Elsevier B.V. All rights reserved.

Birnbaum-Saunders nonlinear regression models

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders distribution. Technometrics 33, 51-60]. We discuss maximum-likelihood estimation for the parameters of the model, and derive closed-form expressions for the second-order biases of these estimates. Our formulae are easily computed as ordinary linear regressions and are then used to define bias corrected maximum-likelihood estimates. Some simulation results show that the bias correction scheme yields nearly unbiased estimates without increasing the mean squared errors. Two empirical applications are analysed and discussed. Crown Copyright (C) 2009 Published by Elsevier B.V. All rights reserved.

Modeling and simulation of the anode in direct ethanol fuels cells

Mathematical modeling has been extensively applied to the study and development of fuel cells. In this work, the objective is to characterize a mechanistic model for the anode of a direct ethanol fuel cell and perform appropriate simulations. The software Comsol Multiphysics (R) (and the Chemical Engineering Module) was used in this work. The software Comsol Multiphysics (R) is an interactive environment for modeling scientific and engineering applications using partial differential equations (PDEs). Based on the finite element method, it provides speed and accuracy for several applications. The mechanistic model developed here can supply details of the physical system, such as the concentration profiles of the components within the anode and the coverage of the adsorbed species on the electrode surface. Also, the anode overpotential-current relationship can be obtained. To validate the anode model presented in this paper, experimental data obtained with a single fuel cell operating with an ethanol solution at the anode were used. (C) 2008 Elsevier B.V. All rights reserved.

Técnicas de diagnóstico de influência local na análise espacial da produtividade da soja

A modelagem da estrutura de dependência espacial pela abordagem da geoestatística é fundamental para a definição de parâmetros que definem esta estrutura, e que são utilizados na interpolação de valores em locais não amostrados pela técnica de krigagem. Entretanto, a estimação de parâmetros pode ser muito afetada pela presença de observações atípicas nos dados amostrados. O desenvolvimento deste trabalho teve por objetivo utilizar técnicas de diagnóstico de influência local em modelos espaciais lineares gaussianos, utilizados em geoestatística, para avaliar a sensibilidade dos estimadores de máxima verossimilhança e máxima verossimilhança restrita na presença de dados discrepantes. Estudos com dados experimentais mostraram que tanto a presença de valores atípicos como de valores considerados influentes, pela análise de diagnóstico, pode exercer forte influência nos mapas temáticos, alterando, assim, a estrutura de dependência espacial. As aplicações de técnicas de diagnóstico de influência local devem fazer parte de toda análise geoestatística a fim de garantir que as informações contidas nos mapas temáticos tenham maior qualidade e possam ser utilizadas com maior segurança pelo agricultor.

Exact time-dependent solutions for a self-regulating gene

The exact time-dependent solution for the stochastic equations governing the behavior of a binary self-regulating gene is presented. Using the generating function technique to rephrase the master equations in terms of partial differential equations, we show that the model is totally integrable and the analytical solutions are the celebrated confluent Heun functions. Self-regulation plays a major role in the control of gene expression, and it is remarkable that such a microscopic model is completely integrable in terms of well-known complex functions.

Genomic islands in the pathogenic filamentous fungus Aspergillus fumigatus

We present the genome sequences of a new clinical isolate of the important human pathogen, Aspergillus fumigatus, A1163, and two closely related but rarely pathogenic species, Neosartorya fischeri NRRL181 and Aspergillus clavatus NRRL1. Comparative genomic analysis of A1163 with the recently sequenced A. fumigatus isolate Af293 has identified core, variable and up to 2% unique genes in each genome. While the core genes are 99.8% identical at the nucleotide level, identity for variable genes can be as low 40%. The most divergent loci appear to contain heterokaryon incompatibility ( het) genes associated with fungal programmed cell death such as developmental regulator rosA. Cross-species comparison has revealed that 8.5%, 13.5% and 12.6%, respectively, of A. fumigatus, N. fischeri and A. clavatus genes are species-specific. These genes are significantly smaller in size than core genes, contain fewer exons and exhibit a subtelomeric bias. Most of them cluster together in 13 chromosomal islands, which are enriched for pseudogenes, transposons and other repetitive elements. At least 20% of A. fumigatus-specific genes appear to be functional and involved in carbohydrate and chitin catabolism, transport, detoxification, secondary metabolism and other functions that may facilitate the adaptation to heterogeneous environments such as soil or a mammalian host. Contrary to what was suggested previously, their origin cannot be attributed to horizontal gene transfer ( HGT), but instead is likely to involve duplication, diversification and differential gene loss (DDL). The role of duplication in the origin of lineage-specific genes is further underlined by the discovery of genomic islands that seem to function as designated ""gene dumps'' and, perhaps, simultaneously, as "" gene factories''.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.