Local Influence Analysis for Skew-Normal Linear Mixed Models

In this article, we consider local influence analysis for the skew-normal linear mixed model (SN-LMM). As the observed data log-likelihood associated with the SN-LMM is intractable, Cook`s well-known approach cannot be applied to obtain measures of local influence. Instead, we develop local influence measures following the approach of Zhu and Lee (2001). This approach is based on the use of an EM-type algorithm and is measurement invariant under reparametrizations. Four specific perturbation schemes are discussed. Results obtained for a simulated data set and a real data set are reported, illustrating the usefulness of the proposed methodology.

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.

Bayesian density estimation using Skew Student-t-Normal mixtures

We present a Bayesian approach for modeling heterogeneous data and estimate multimodal densities using mixtures of Skew Student-t-Normal distributions [Gomez, H.W., Venegas, O., Bolfarine, H., 2007. Skew-symmetric distributions generated by the distribution function of the normal distribution. Environmetrics 18, 395-407]. A stochastic representation that is useful for implementing a MCMC-type algorithm and results about existence of posterior moments are obtained. Marginal likelihood approximations are obtained, in order to compare mixture models with different number of component densities. Data sets concerning the Gross Domestic Product per capita (Human Development Report) and body mass index (National Health and Nutrition Examination Survey), previously studied in the related literature, are analyzed. (c) 2008 Elsevier B.V. All rights reserved.

Skew-normal linear calibration: a Bayesian perspective

In this paper, we present a Bayesian approach for estimation in the skew-normal calibration model, as well as the conditional posterior distributions which are useful for implementing the Gibbs sampler. Data transformation is thus avoided by using the methodology proposed. Model fitting is implemented by proposing the asymmetric deviance information criterion, ADIC, a modification of the ordinary DIC. We also report an application of the model studied by using a real data set, related to the relationship between the resistance and the elasticity of a sample of concrete beams. Copyright (C) 2008 John Wiley & Sons, Ltd.

Bias correction in a multivariate normal regression model with general parameterization

This paper derives the second-order biases Of maximum likelihood estimates from a multivariate normal model where the mean vector and the covariance matrix have parameters in common. We show that the second order bias can always be obtained by means of ordinary weighted least-squares regressions. We conduct simulation studies which indicate that the bias correction scheme yields nearly unbiased estimators. (C) 2009 Elsevier B.V. All rights reserved.

Distinguishing DDoS attacks from flash crowds using probability metrics

Both Flash crowds and DDoS (Distributed Denial-of-Service) attacks have very similar properties in terms of internet traffic, however Flash crowds are legitimate flows and DDoS attacks are illegitimate flows, and DDoS attacks have been a serious threat to internet security and stability. In this paper we propose a set of novel methods using probability metrics to distinguish DDoS attacks from Flash crowds effectively, and our simulations show that the proposed methods work well. In particular, these mathods can not only distinguish DDoS attacks from Flash crowds clearly, but also can distinguish the anomaly flow being DDoS attacks flow or being Flash crowd flow from Normal network flow effectively. Furthermore, we show our proposed hybrid probability metrics can greatly reduce both false positive and false negative rates in detection.

The cost-effectiveness of the Dose Adjustment for Normal Eating (DAFNE) structured education programme: an update using the Sheffield Type 1 Diabetes policy model

AIMS: 
To estimate the cost-effectiveness of training in flexible intensive insulin therapy [as provided in the Dose Adjustment for Normal Eating (DAFNE) structured education programme] compared with no training for adults with Type 1 diabetes mellitus in the UK using the Sheffield Type 1 Diabetes Policy Model.

METHODS: 
The Sheffield Type 1 Diabetes Policy Model was used to simulate the development of long-term microvascular and macrovascular diabetes-related complications and the occurrence of diabetes-related adverse events in 5000 adults with Type 1 diabetes. Total costs and quality-adjusted life years were estimated from a National Health Service perspective over a lifetime horizon, discounted at a rate of 3.5%. The treatment effectiveness of DAFNE was modelled as a reduction in HbA1c that affected the risk of developing long-term diabetes-related complications. Probabilistic and structural sensitivity analyses were conducted.

RESULTS:
DAFNE resulted in greater life expectancy and reduced incidence of some diabetes-related complications compared with no DAFNE. DAFNE was found to generate an average of 0.0294 additional quality-adjusted life years for an additional cost of £426 per patient, leading to an incremental cost-effectiveness ratio of £14 400 compared with no DAFNE. There was a 54% probability that DAFNE would be cost-effective at a willingness-to-pay threshold of £20 000 per quality-adjusted life year.

CONCLUSIONS: 
The results of this study suggest that DAFNE is a cost-effective structured education programme for people with Type 1 diabetes and support its provision by the National Health Service in the UK.

Síndrome metabólica e fatores associados: estudo comparativo com mulheres que apresentaram pré-eclâmpsia e gravidez normal, acompanhadas cinco anos após o parto

Preeclampsia is defined as an extremely serious complication of the pregnancy-puerperium cycle with delayed emergence of cardiovascular risk factors, including metabolic syndrome. The research aimed estimate the prevalences of metabolic syndrome and associated factors in women with preeclampsia and normal pregnancy followed five years after childbirth. This is a cross-sectional observational study using a quantitative approach, conducted at a maternity school in the city of Natal in Rio Grande do Norte state. The sample was composed of 70 women with previous preeclampsia and 75 normal selected by simple random probability sampling. Subjects were analyzed for sociodemographic, obstetric, clinical, anthropometric and biochemical parameters. International Diabetes Federation criteria were adopted to diagnose metabol ic syndrome. The Kolmogorov-Smirnov, Mann-Whitney, Student s t, Pearson s chi-squared, and Fisher s exact tests, in addition to simple logistic regression, were used for data analysis, at a 5% significance level (p ≤ 0.05). Statistical tests demonstrated elevated body mass index (p = 0.001), predominance of family history of diabetes mellitus (p = 0.022) and significantly higher prevalence of metabolic syndrome in the preeclampsia group (37.1%) when compared to normal (22.7%) (p = 0.042). Intergroup comparison showed a high number of metabolic syndrome components in women with previous preeclampsia. Altered systolic and diastolic blood pressure (p < 0.001) was the most prevalent, followed by low concentrations of high-density lipoproteins (p = 0.049), and hyperglycemia (p=0.030). There was a predominance of the metabolic syndrome in women with schooling 0-9 years (42.4%) (p = 0.005), body mass index above 30Kg.m 2 (52.3%) (p < 0.001), uric acid high (62.5%) (p = 0.050 and family history of hypertension (38.5%) (p< 0.001). Multivariate analysis of the data showed that the body mass index above 30 kg.m2, education level less than 10 years of study (p < 0.001) and family history of hypertension (p = 0.002) remained associated with the metabolic syndrome after multivariate analysis of the data. It is considered Women with previous preeclampsia exhibited high prevalence of metabolic syndrome and their individual components in relation to normal, especially, altered systolic and diastolic blood pressure, low concentrations of high-density lipoproteins and hyperglycemia. The factors associated to this ou tcome were obesity, less than 10 years of schooling, and family history of hypertension. Overall, this study identified young women with a history of PE exposed to a higher cardiovascular risk than normal

Misclassification probability as obese or lean in hypercaloric and normocaloric diet

The aim of the present study was to determine the classification error probabilities, as lean or obese, in hypercaloric diet-induced obesity, which depends on the variable used to characterize animal obesity. In addition, the misclassification probabilities in animals submitted to normocaloric diet were also evaluated. Male Wistar rats were randomly distributed into two groups: normal diet (ND; n=3 1; 3,5 Kcal/g) and hypercaloric diet (HD; n=31; 4,6 Kcal/g). The ND group received commercial Labina rat feed and HD animals a cycle of five hypercaloric diets for a 14-week period. The variables analysed were body weight, body composition, body weight to length ratio, Lee index, body mass index and misclassification probability A 5% significance level was used. The hypercaloric pellet-diet cycle promoted increase of body weight, carcass fat, body weight to length ratio and Lee index. The total misclassification probabilities ranged from 19.21 % to 40.91 %. In Conclusion, the results of this experiment show that rnisclassification probabilities Occur when dietary manipulation is used to promote obesity in animals. This misjudgement ranges from 19.49% to 40.52% in hypercaloric diet and 18.94% to 41.30% in normocaloric diet.

A Generalized Log-Normal Model for Grouped Survival Data

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Sexual Precocity of Nellore Bulls that are Offspring of Super Precocious, Precocious and Normal Cows in Extensive Farming Conditions

Contents The objective of this work was to verify that mothers classified as super precocious (M1) and precocious (M2) produce more precocious bulls than females classified as normal (M3). This study included 21186 animals with an average age of 21.29 +/- 1.77months that underwent a breeding soundness evaluation from 1999 to 2008. Of these animals, 2019, 6059 and 13108 were offspring of M1, M2 and M3 females, respectively. In the breeding soundness examination, the animals were classified as sound for reproduction, sound under a natural mating regime, unsound for reproduction and discarded. To compare the averages obtained for each category of mother within the individual breeding soundness classes, a chi-square test with a 5% error probability was used, considering the effects of year and month of birth and farm. For the three classes of mothers (M1, M2 and M3), 67.26, 67.22 and 64.16% of bull calves were considered sound for reproduction and 19.71, 19.46 and 21.90% were considered unsound for reproduction, respectively. There was no difference in the frequency of animals that were sound for reproduction under the natural breeding regime between the three classes of mothers (8.87, 9.31 and 9.19%, respectively). There was a difference between the numbers of precocious and normal females that were discarded, with frequencies of 4.01 and 4.75%, respectively (p<0.05). There were differences in year and month of birth and farm between super precocious and precocious cows in relation to the breeding soundness classification of the animals. It was concluded that the bull offspring of super precocious and precocious cows presented a higher percentage of approval in the breeding soundness examination than the bull offspring of normal cows, demonstrating that the selection for precocity of females has contributed to an increase in the sexual precocity of the herd in relation to the sexual maturity of bulls.

Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions

An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. This novel class of models provides a useful generalization of the heteroscedastic symmetrical nonlinear regression models (Cysneiros et al., 2010), since the random term distributions cover both symmetric as well as asymmetric and heavy-tailed distributions such as skew-t, skew-slash, skew-contaminated normal, among others. A simple EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters is presented and the observed information matrix is derived analytically. In order to examine the performance of the proposed methods, some simulation studies are presented to show the robust aspect of this flexible class against outlying and influential observations and that the maximum likelihood estimates based on the EM-type algorithm do provide good asymptotic properties. Furthermore, local influence measures and the one-step approximations of the estimates in the case-deletion model are obtained. Finally, an illustration of the methodology is given considering a data set previously analyzed under the homoscedastic skew-t nonlinear regression model. (C) 2012 Elsevier B.V. All rights reserved.

An extension of the half-normal distribution

In this paper we introduce a new distribution, namely, the slashed half-normal distribution and it can be seen as an extension of the half-normal distribution. It is shown that the resulting distribution has more kurtosis than the ordinary half-normal distribution. Moments and some properties are derived for the new distribution. Moment estimators and maximum likelihood estimators can computed using numerical procedures. Results of two real data application are reported where model fitting is implemented by using maximum likelihood estimation. The applications illustrate the better performance of the new distribution.

Parameter recovery for a skew-normal IRT model under a Bayesian approach: hierarchical framework, prior and kernel sensitivity and sample size

Item response theory (IRT) comprises a set of statistical models which are useful in many fields, especially when there is an interest in studying latent variables (or latent traits). Usually such latent traits are assumed to be random variables and a convenient distribution is assigned to them. A very common choice for such a distribution has been the standard normal. Recently, Azevedo et al. [Bayesian inference for a skew-normal IRT model under the centred parameterization, Comput. Stat. Data Anal. 55 (2011), pp. 353-365] proposed a skew-normal distribution under the centred parameterization (SNCP) as had been studied in [R. B. Arellano-Valle and A. Azzalini, The centred parametrization for the multivariate skew-normal distribution, J. Multivariate Anal. 99(7) (2008), pp. 1362-1382], to model the latent trait distribution. This approach allows one to represent any asymmetric behaviour concerning the latent trait distribution. Also, they developed a Metropolis-Hastings within the Gibbs sampling (MHWGS) algorithm based on the density of the SNCP. They showed that the algorithm recovers all parameters properly. Their results indicated that, in the presence of asymmetry, the proposed model and the estimation algorithm perform better than the usual model and estimation methods. Our main goal in this paper is to propose another type of MHWGS algorithm based on a stochastic representation (hierarchical structure) of the SNCP studied in [N. Henze, A probabilistic representation of the skew-normal distribution, Scand. J. Statist. 13 (1986), pp. 271-275]. Our algorithm has only one Metropolis-Hastings step, in opposition to the algorithm developed by Azevedo et al., which has two such steps. This not only makes the implementation easier but also reduces the number of proposal densities to be used, which can be a problem in the implementation of MHWGS algorithms, as can be seen in [R.J. Patz and B.W. Junker, A straightforward approach to Markov Chain Monte Carlo methods for item response models, J. Educ. Behav. Stat. 24(2) (1999), pp. 146-178; R. J. Patz and B. W. Junker, The applications and extensions of MCMC in IRT: Multiple item types, missing data, and rated responses, J. Educ. Behav. Stat. 24(4) (1999), pp. 342-366; A. Gelman, G.O. Roberts, and W.R. Gilks, Efficient Metropolis jumping rules, Bayesian Stat. 5 (1996), pp. 599-607]. Moreover, we consider a modified beta prior (which generalizes the one considered in [3]) and a Jeffreys prior for the asymmetry parameter. Furthermore, we study the sensitivity of such priors as well as the use of different kernel densities for this parameter. Finally, we assess the impact of the number of examinees, number of items and the asymmetry level on the parameter recovery. Results of the simulation study indicated that our approach performed equally as well as that in [3], in terms of parameter recovery, mainly using the Jeffreys prior. Also, they indicated that the asymmetry level has the highest impact on parameter recovery, even though it is relatively small. A real data analysis is considered jointly with the development of model fitting assessment tools. The results are compared with the ones obtained by Azevedo et al. The results indicate that using the hierarchical approach allows us to implement MCMC algorithms more easily, it facilitates diagnosis of the convergence and also it can be very useful to fit more complex skew IRT models.

A Bootstrap Test for the Probability of Ruin in the Compound Poisson Risk Process

In this article we propose a bootstrap test for the probability of ruin in the compound Poisson risk process. We adopt the P-value approach, which leads to a more complete assessment of the underlying risk than the probability of ruin alone. We provide second-order accurate P-values for this testing problem and consider both parametric and nonparametric estimators of the individual claim amount distribution. Simulation studies show that the suggested bootstrap P-values are very accurate and outperform their analogues based on the asymptotic normal approximation.