Improved maximum-likelihood estimation in a regression model with general parametrization

We analyse the finite-sample behaviour of two second-order bias-corrected alternatives to the maximum-likelihood estimator of the parameters in a multivariate normal regression model with general parametrization proposed by Patriota and Lemonte [A. G. Patriota and A. J. Lemonte, Bias correction in a multivariate regression model with genereal parameterization, Stat. Prob. Lett. 79 (2009), pp. 1655-1662]. The two finite-sample corrections we consider are the conventional second-order bias-corrected estimator and the bootstrap bias correction. We present the numerical results comparing the performance of these estimators. Our results reveal that analytical bias correction outperforms numerical bias corrections obtained from bootstrapping schemes.

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.

A bivariate regression model for matched paired survival data: local influence and residual analysis

The use of bivariate distributions plays a fundamental role in survival and reliability studies. In this paper, we consider a location scale model for bivariate survival times based on the proposal of a copula to model the dependence of bivariate survival data. For the proposed model, we consider inferential procedures based on maximum likelihood. Gains in efficiency from bivariate models are also examined in the censored data setting. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the bivariate regression model for matched paired survival data. Sensitivity analysis methods such as local and total influence are presented and derived under three perturbation schemes. The martingale marginal and the deviance marginal residual measures are used to check the adequacy of the model. Furthermore, we propose a new measure which we call modified deviance component residual. The methodology in the paper is illustrated on a lifetime data set for kidney patients.

A nonlinear regression model with skew-normal errors

In this paper we have discussed inference aspects of the skew-normal nonlinear regression models following both, a classical and Bayesian approach, extending the usual normal nonlinear regression models. The univariate skew-normal distribution that will be used in this work was introduced by Sahu et al. (Can J Stat 29:129-150, 2003), which is attractive because estimation of the skewness parameter does not present the same degree of difficulty as in the case with Azzalini (Scand J Stat 12:171-178, 1985) one and, moreover, it allows easy implementation of the EM-algorithm. As illustration of the proposed methodology, we consider a data set previously analyzed in the literature under normality.

The log-exponentiated Weibull regression model for interval-censored data

In interval-censored survival data, the event of interest is not observed exactly but is only known to occur within some time interval. Such data appear very frequently. In this paper, we are concerned only with parametric forms, and so a location-scale regression model based on the exponentiated Weibull distribution is proposed for modeling interval-censored data. We show that the proposed log-exponentiated Weibull regression model for interval-censored data represents a parametric family of models that include other regression models that are broadly used in lifetime data analysis. Assuming the use of interval-censored data, we employ a frequentist analysis, a jackknife estimator, a parametric bootstrap and a Bayesian analysis for the parameters of the proposed model. We derive the appropriate matrices for assessing local influences on the parameter estimates under different perturbation schemes and present some ways to assess global influences. Furthermore, for different parameter settings, sample sizes and censoring percentages, various simulations are performed; in addition, the empirical distribution of some modified residuals are displayed and compared with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to a modified deviance residual in log-exponentiated Weibull regression models for interval-censored data. (C) 2009 Elsevier B.V. All rights reserved.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Signed likelihood ratio tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders regression model is becoming increasingly popular in lifetime analyses and reliability studies. In this model, the signed likelihood ratio statistic provides the basis for testing inference and construction of confidence limits for a single parameter of interest. We focus on the small sample case, where the standard normal distribution gives a poor approximation to the true distribution of the statistic. We derive three adjusted signed likelihood ratio statistics that lead to very accurate inference even for very small samples. Two empirical applications are presented. (C) 2010 Elsevier B.V. All rights reserved.

Bayesian Analysis for Nonlinear Regression Model Under Skewed Errors, with Application in Growth Curves

We have considered a Bayesian approach for the nonlinear regression model by replacing the normal distribution on the error term by some skewed distributions, which account for both skewness and heavy tails or skewness alone. The type of data considered in this paper concerns repeated measurements taken in time on a set of individuals. Such multiple observations on the same individual generally produce serially correlated outcomes. Thus, additionally, our model does allow for a correlation between observations made from the same individual. We have illustrated the procedure using a data set to study the growth curves of a clinic measurement of a group of pregnant women from an obstetrics clinic in Santiago, Chile. Parameter estimation and prediction were carried out using appropriate posterior simulation schemes based in Markov Chain Monte Carlo methods. Besides the deviance information criterion (DIC) and the conditional predictive ordinate (CPO), we suggest the use of proper scoring rules based on the posterior predictive distribution for comparing models. For our data set, all these criteria chose the skew-t model as the best model for the errors. These DIC and CPO criteria are also validated, for the model proposed here, through a simulation study. As a conclusion of this study, the DIC criterion is not trustful for this kind of complex model.

South Atlantic Ocean cyclogenesis climatology simulated by regional climate model (RegCM3)

A detailed climatology of the cyclogenesis over the Southern Atlantic Ocean (SAO) from 1990 to 1999 and how it is simulated by the RegCM3 (Regional Climate Model) is presented here. The simulation used as initial and boundary conditions the National Centers for Environmental Prediction-Department of Energy (NCEP/DOE) reanalysis. The cyclones were identified with an automatic scheme that searches for cyclonic relative vorticity (zeta(10)) obtained from a 10-m height wind field. All the systems with zeta(10) a parts per thousand currency sign -1.5 x 10(-5) s(-1) and lifetime equal or larger than 24 h were considered in the climatology. Over SAO, in 10 years were detected 2,760 and 2,787 cyclogeneses in the simulation and NCEP, respectively, with an annual mean of 276.0 +/- A 11.2 and 278.7 +/- A 11.1. This result suggests that the RegCM3 has a good skill to simulate the cyclogenesis climatology. However, the larger model underestimations (-9.8%) are found for the initially stronger systems (zeta(10) a parts per thousand currency sign -2.5 x 10(-5) s(-1)). It was noted that over the SAO the annual cycle of the cyclogenesis depends of its initial intensity. Considering the systems initiate with zeta(10) a parts per thousand currency sign -1.5 x 10(-5) s(-1), the annual cycle is not well defined and the higher frequency occurs in the autumn (summer) in the NCEP (RegCM3). The stronger systems (zeta(10) a parts per thousand currency sign -2.5 x 10(-5) s(-1)) have a well-characterized high frequency of cyclogenesis during the winter in both NCEP and RegCM3. This work confirms the existence of three cyclogenetic regions in the west sector of the SAO, near the South America east coast and shows that RegCM3 is able to reproduce the main features of these cyclogenetic areas.

IPCC global coupled model simulations of the South America monsoon system

This study examines the variability of the South America monsoon system (SAMS) over tropical South America (SA). The onset, end, and total rainfall during the summer monsoon are investigated using precipitation pentad estimates from the global precipitation climatology project (GPCP) 1979-2006. Likewise, the variability of SAMS characteristics is examined in ten Intergovernmental Panel on Climate Change (IPCC) global coupled climate models in the twentieth century (1981-2000) and in a future scenario of global change (A1B) (2081-2100). It is shown that most IPCC models misrepresent the intertropical convergence zone and therefore do not capture the actual annual cycle of precipitation over the Amazon and northwest SA. Most models can correctly represent the spatiotemporal variability of the annual cycle of precipitation in central and eastern Brazil such as the correct phase of dry and wet seasons, onset dates, duration of rainy season and total accumulated precipitation during the summer monsoon for the twentieth century runs. Nevertheless, poor representation of the total monsoonal precipitation over the Amazon and northeast Brazil is observed in a large majority of the models. Overall, MI-ROC3.2-hires, MIROC3.2-medres and MRI-CGCM3.2.3 show the most realistic representation of SAMS`s characteristics such as onset, duration, total monsoonal precipitation, and its interannual variability. On the other hand, ECHAM5, GFDL-CM2.0 and GFDL-CM2.1 have the least realistic representation of the same characteristics. For the A1B scenario the most coherent feature observed in the IPCC models is a reduction in precipitation over central-eastern Brazil during the summer monsoon, comparatively with the present climate. The IPCC models do not indicate statistically significant changes in SAMS onset and demise dates for the same scenario.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

Hypotheses Testing on a Multivariate Null Intercept Errors-in-Variables Model

Considering the Wald, score, and likelihood ratio asymptotic test statistics, we analyze a multivariate null intercept errors-in-variables regression model, where the explanatory and the response variables are subject to measurement errors, and a possible structure of dependency between the measurements taken within the same individual are incorporated, representing a longitudinal structure. This model was proposed by Aoki et al. (2003b) and analyzed under the bayesian approach. In this article, considering the classical approach, we analyze asymptotic test statistics and present a simulation study to compare the behavior of the three test statistics for different sample sizes, parameter values and nominal levels of the test. Also, closed form expressions for the score function and the Fisher information matrix are presented. We consider two real numerical illustrations, the odontological data set from Hadgu and Koch (1999), and a quality control data set.

Bayesian analysis for a skew extension of the multivariate null intercept measurement error model

Skew-normal distribution is a class of distributions that includes the normal distributions as a special case. In this paper, we explore the use of Markov Chain Monte Carlo (MCMC) methods to develop a Bayesian analysis in a multivariate, null intercept, measurement error model [R. Aoki, H. Bolfarine, J.A. Achcar, and D. Leao Pinto Jr, Bayesian analysis of a multivariate null intercept error-in -variables regression model, J. Biopharm. Stat. 13(4) (2003b), pp. 763-771] where the unobserved value of the covariate (latent variable) follows a skew-normal distribution. The results and methods are applied to a real dental clinical trial presented in [A. Hadgu and G. Koch, Application of generalized estimating equations to a dental randomized clinical trial, J. Biopharm. Stat. 9 (1999), pp. 161-178].

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.