Inference and local influence assessment in skew-normal null intercept measurement error model

In this article, we discuss inferential aspects of the measurement error regression models with null intercepts when the unknown quantity x (latent variable) follows a skew normal distribution. We examine first the maximum-likelihood approach to estimation via the EM algorithm by exploring statistical properties of the model considered. Then, the marginal likelihood, the score function and the observed information matrix of the observed quantities are presented allowing direct inference implementation. In order to discuss some diagnostics techniques in this type of models, we derive the appropriate matrices to assessing the local influence on the parameter estimates under different perturbation schemes. The results and methods developed in this paper are illustrated considering part of a real data set used by Hadgu and Koch [1999, Application of generalized estimating equations to a dental randomized clinical trial. Journal of Biopharmaceutical Statistics, 9, 161-178].

Likelihood ratio tests for variance components in linear mixed models

Although the asymptotic distributions of the likelihood ratio for testing hypotheses of null variance components in linear mixed models derived by Stram and Lee [1994. Variance components testing in longitudinal mixed effects model. Biometrics 50, 1171-1177] are valid, their proof is based on the work of Self and Liang [1987. Asymptotic properties of maximum likelihood estimators and likelihood tests under nonstandard conditions. J. Amer. Statist. Assoc. 82, 605-610] which requires identically distributed random variables, an assumption not always valid in longitudinal data problems. We use the less restrictive results of Vu and Zhou [1997. Generalization of likelihood ratio tests under nonstandard conditions. Ann. Statist. 25, 897-916] to prove that the proposed mixture of chi-squared distributions is the actual asymptotic distribution of such likelihood ratios used as test statistics for null variance components in models with one or two random effects. We also consider a limited simulation study to evaluate the appropriateness of the asymptotic distribution of such likelihood ratios in moderately sized samples. (C) 2008 Elsevier B.V. All rights reserved.

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.

Hypothesis testing in an errors-in-variables model with heteroscedastic measurement errors

In many epidemiological studies it is common to resort to regression models relating incidence of a disease and its risk factors. The main goal of this paper is to consider inference on such models with error-prone observations and variances of the measurement errors changing across observations. We suppose that the observations follow a bivariate normal distribution and the measurement errors are normally distributed. Aggregate data allow the estimation of the error variances. Maximum likelihood estimates are computed numerically via the EM algorithm. Consistent estimation of the asymptotic variance of the maximum likelihood estimators is also discussed. Test statistics are proposed for testing hypotheses of interest. Further, we implement a simple graphical device that enables an assessment of the model`s goodness of fit. Results of simulations concerning the properties of the test statistics are reported. The approach is illustrated with data from the WHO MONICA Project on cardiovascular disease. Copyright (C) 2008 John Wiley & Sons, Ltd.

The log-bimodal-skew-normal model. A geochemical application

The main objective of this paper is to study a logarithm extension of the bimodal skew normal model introduced by Elal-Olivero et al. [1]. The model can then be seen as an alternative to the log-normal model typically used for fitting positive data. We study some basic properties such as the distribution function and moments, and discuss maximum likelihood for parameter estimation. We report results of an application to a real data set related to nickel concentration in soil samples. Model fitting comparison with several alternative models indicates that the model proposed presents the best fit and so it can be quite useful in real applications for chemical data on substance concentration. Copyright (C) 2011 John Wiley & Sons, Ltd.

DIAGNOSTIC TECHNIQUES OF LOCAL INFLUENCE IN SPATIAL ANALYSIS OF SOYBEAN YIELD

Modeling of spatial dependence structure, concerning geoestatistics approach, is an indispensable tool for fixing parameters that define this structure, applied on interpolation of values in places that are not sampled, by kriging techniques. However, the estimation of parameters can be greatly affected by the presence of atypical observations on sampled data. Thus, this trial aimed at using diagnostics techniques of local influence in spatial linear Gaussians models, applied at geoestatistics in order to evaluate sensitivity of maximum likelihood estimators and restrict maximum likelihood to small perturbations in these data. So, studies with simulated and experimental data were performed. Those results, obtained from the study of real data, allowed us to conclude that the presence of atypical values among the sampled data can have a strong influence on thematic maps, changing, therefore, the spatial dependence. The application of diagnostics techniques of local influence should be part of any geoestatistic analysis, ensuring that the information from thematic maps has better quality and can be used with greater security by farmers.

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

Feasible estimation of generalized linear mixed models (GLMM) with weak dependency between groups

This paper presents a two-step pseudo likelihood estimation technique for generalized linear mixed models with the random effects being correlated between groups. The core idea is to deal with the intractable integrals in the likelihood function by multivariate Taylor's approximation. The accuracy of the estimation technique is assessed in a Monte-Carlo study. An application of it with a binary response variable is presented using a real data set on credit defaults from two Swedish banks. Thanks to the use of two-step estimation technique, the proposed algorithm outperforms conventional pseudo likelihood algorithms in terms of computational time.

Factors affecting the technical efficiency of production of the Brazilian banking system : a comparison of four statistical models in the context of data envelopment analysis

This paper uses an output oriented Data Envelopment Analysis (DEA) measure of technical efficiency to assess the technical efficiencies of the Brazilian banking system. Four approaches to estimation are compared in order to assess the significance of factors affecting inefficiency. These are nonparametric Analysis of Covariance, maximum likelihood using a family of exponential distributions, maximum likelihood using a family of truncated normal distributions, and the normal Tobit model. The sole focus of the paper is on a combined measure of output and the data analyzed refers to the year 2001. The factors of interest in the analysis and likely to affect efficiency are bank nature (multiple and commercial), bank type (credit, business, bursary and retail), bank size (large, medium, small and micro), bank control (private and public), bank origin (domestic and foreign), and non-performing loans. The latter is a measure of bank risk. All quantitative variables, including non-performing loans, are measured on a per employee basis. The best fits to the data are provided by the exponential family and the nonparametric Analysis of Covariance. The significance of a factor however varies according to the model fit although it can be said that there is some agreements between the best models. A highly significant association in all models fitted is observed only for nonperforming loans. The nonparametric Analysis of Covariance is more consistent with the inefficiency median responses observed for the qualitative factors. The findings of the analysis reinforce the significant association of the level of bank inefficiency, measured by DEA residuals, with the risk of bank failure.

Genetic parameters and environmental effects on temperament score and reproductive traits of Nellore cattle

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estimativas de parâmetros genéticos para os escores visuais e suas associações com peso corporal em bovinos de corte

Foram avaliados 27.523 e 21.746 registros das características conformação, precocidade e musculatura à desmana e ao sobreano, respectivamente, para estimar os componentes de covariância entre estas características e entre estas e os pesos corporais medidos nas mesmas idades. Para as análises dos dados, foram empregados modelos animais com efeitos genéticos direto e materno e efeito de ambiente permanente materno. Máxima verossimilhança restrita foi empregada para estimar os parâmetros genéticos. As estimativas de herdabilidade dos escores à desmama foram 0,13; 0,25 e 0,23 para conformação, precocidade e musculatura, respectivamente. As estimativas de herdabilidade dos escores visuais avaliados ao sobreano foram de maiores magnitudes (0,24; 0,32 e 0,27 para conformação, precocidade e musculatura, respectivamente). As estimativas das correlações genéticas entre escores medidos às mesmas idades, considerando desmana e sobreano, foram 0,67 e 0,75 entre conformação e precocidade; 0,61 e 0,71 entre conformação e musculatura; 0,95 e 0,95 entre precocidade e musculatura. As correlações genéticas estimadas entre o peso corporal à desmama e conformação, precocidade e musculatura, respectivamente, foram 0,97; 0,67 e 0, 62. As estimativas entre conformação, precocidade, musculatura ao sobreano e o peso corporal foram 0,83; 0,59 e 0,58, respectivamente. Os resultados indicam que os escores visuais podem ser utilizados como critérios de seleção. Aumento nos pesos corporais deve ser esperado como resposta correlacionada à seleção para essas características.

Genetic parameters for milk yield analyzed by test-day models in Murrah buffaloes in Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Random regression models using different functions to model test-day milk yield of Brazilian Holstein cows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Heterogeneidade dos componentes de variância na produção de leite e seus efeitos nas estimativas de herdabilidade e repetibilidade

It was evaluated the heterogeneity of components of phenotypic variance and its effects on the heritability and repeatability estimates for milk yield in Holstein cattle. The herds were grouped according to their level of production (low, medium and high) and evaluated in the non-transformed, square-root and logarithmic scale. Variance components were estimated using a restricted maximum likelihood method based on an animal model that included fixed effects of herd-year-season, and as covariates the linear effect of lactation duration and the linear and quadratic effects of cow's age at calving and the random direct additive genetic, permanent environment and residual effects. In the non-transformed scale all the variance components were heterogeneous. on this scale, residual and phenotypic variance components were associated positively with the level of production while in logarithmic scale that association was negative. Estimates of heritability were more affected than the repeatability for the phenotypic variance heterogeneity and their components. The of selection process efficiency for milk production could be affected by the level of production which was considered for genetic parameters estimation.

Estudo das precipitações máximas anuais em Presidente Prudente

Considerando a importância sócio-econômica da região de Presidente Prudente, este estudo teve como objetivo estimar a precipitação pluvial máxima esperada para diferentes níveis de probabilidade e verificar o grau de ajuste dos dados ao modelo Gumbel, com as estimativas dos parâmetros obtidas pelo método de máxima verossimilhança. Pelos resultados, o teste de Kolmogorov-Sminorv (K-S) mostrou que a distribuição Gumbel testada se ajustou com p-valor maior que 0.28 para todos os períodos de tempo considerados, comprovando que a distribuição Gumbel apresenta um bom ajustamento aos dados observados para representar as precipitações pluviais máximas. As estimativas de precipitação obtidas pelo método de máxima verossimilhança são consistentes, conseguindo reproduzir com bastante fidelidade o regime de chuvas da região de Presidente Prudente. Assim, o conhecimento da distribuição da precipitação pluvial máxima mensal e das estimativas das precipitações diárias máximas esperadas, possibilita um planejamento estratégico melhor, minimizando assim o risco de ocorrência de perdas econômicas para essa região.