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.

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.

NeXSPheRIO results on azimuthal anisotropy in Au-Au collisions at 200 A GeV

In this work, we present the results obtained by the hydrodynamic code NeXSPheRIO on anisotropic flows. In our calculation, we made use of event-by-event fluctuating initial conditions and chemical freeze-out was explicitly implemented. We studied directed flow, elliptic flow and forth harmonic coefficient for various hadrons at different centrality windows for Au+Au collisions at 200 A GeV. The results are discussed and compared with experimental data from RHIC.

NeXSPheRIO results on elliptic-flow fluctuations at RHIC

By using the NeXSPheRIO code, we study the elliptic-flow fluctuations in Au + Au collisions at 200 A GeV. It is shown that, by fixing the parameters of the model to correctly reproduce the charged pseudorapidity and the transverse-momentum distributions, reasonable agreement of < v(2)> with data is obtained, both as function of pseudorapidity as well as of transverse momentum, for charged particles. Our results on elliptic-flow fluctuations are in good agreement with the recently measured data on experiments.

Restoring the azimuthal symmetry of lateral distributions of charged particles in the range of the KASCADE-Grande experiment

The reconstruction of Extensive Air Showers (EAS) observed by particle detectors at the ground is based on the characteristics of observables like the lateral particle density and the arrival times. The lateral densities, inferred for different EAS components from detector data, are usually parameterised by applying various lateral distribution functions (LDFs). The LDFs are used in turn for evaluating quantities like the total number of particles or the density at particular radial distances. Typical expressions for LDFs anticipate azimuthal symmetry of the density around the shower axis. The deviations of the lateral particle density from this assumption arising from various reasons are smoothed out in the case of compact arrays like KASCADE, but not in the case of arrays like Grande, which only sample a smaller part of the azimuthal variation. KASCADE-Grande, an extension of the former KASCADE experiment, is a multi-component Extensive Air Shower (EAS) experiment located at the Karlsruhe Institute of Technology (Campus North), Germany. The lateral distributions of charged particles are deduced from the basic information provided by the Grande scintillators - the energy deposits - first in the observation plane, then in the intrinsic shower plane. In all steps azimuthal dependences should be taken into account. As the energy deposit in the scintillators is dependent on the angles of incidence of the particles, azimuthal dependences are already involved in the first step: the conversion from the energy deposits to the charged particle density. This is done by using the Lateral Energy Correction Function (LECF) that evaluates the mean energy deposited by a charged particle taking into account the contribution of other particles (e.g. photons) to the energy deposit. By using a very fast procedure for the evaluation of the energy deposited by various particles we prepared realistic LECFs depending on the angle of incidence of the shower and on the radial and azimuthal coordinates of the location of the detector. Mapping the lateral density from the observation plane onto the intrinsic shower plane does not remove the azimuthal dependences arising from geometric and attenuation effects, in particular for inclined showers. Realistic procedures for applying correction factors are developed. Specific examples of the bias due to neglecting the azimuthal asymmetries in the conversion from the energy deposit in the Grande detectors to the lateral density of charged particles in the intrinsic shower plane are given. (C) 2011 Elsevier B.V. All rights reserved.

Cross-situational and supervised learning in the emergence of communication

Scenarios for the emergence or bootstrap of a lexicon involve the repeated interaction between at least two agents who must reach a consensus on how to name N objects using H words. Here we consider minimal models of two types of learning algorithms: cross-situational learning, in which the individuals determine the meaning of a word by looking for something in common across all observed uses of that word, and supervised operant conditioning learning, in which there is strong feedback between individuals about the intended meaning of the words. Despite the stark differences between these learning schemes, we show that they yield the same communication accuracy in the limits of large N and H, which coincides with the result of the classical occupancy problem of randomly assigning N objects to H words.

Tectonic fabric revealed by AARM of the proterozoic mafic dike swarm in the Salvador city (Bahia state): Sao Francisco Craton, NE Brazil

Magnetic fabric and rock magnetism studies were performed on 25 unmetamorphosed mafic dikes of the Meso-Late Proterozoic (similar to 1.02 Ga) dike swarm from Salvador (Bahia State, NE Brazil). This area lies in the north-eastern part of the Sao Francisco Craton, which was dominantly formed/reworked during the Transamazonian orogeny (2.14-1.94 Ga). The dikes crop out along the beaches and in quarries around Salvador city, and cut across both amphibolite dikes and granulites. Their widths range from a few centimeters up to 30 m with an average of similar to 4 m, and show two main trends N 140-190 and N 100-120 with vertical dips. Magnetic fabrics were determined using both anisotropy of low-field magnetic susceptibility (AMS) and anisotropy of anhysteretic remanent magnetization (AARM). The magnetic mineralogy was investigated by many experiments including remanent magnetization measurements at variable low temperatures (10-300 K), Mossbauer spectroscopy, high temperature magnetization curves (25-700 degrees C) and scanning electron microscopy (SEM). The rock magnetism study suggests pseudo-single-domain magnetite grains carrying the bulk magnetic susceptibility and AARM fabrics. The magnetite grains found in these dikes are large and we discard the presence of single-domain grains. Its composition is close to stoichiometric with low Ti substitution, and its Verwey transition occurs around 120 K. The main AMS fabric recognized in the swarm is so-called normal, in which the K(max)-K(int) plane is parallel to the dike plane and the magnetic foliation pole K(min)) is perpendicular to it. This fabric is interpreted as due to magma flow, and analysis of the K m inclination permitted to infer that approximately 80% of the dikes were fed by horizontal or sub-horizontal flows (K(max) < 30 degrees). This interpretation is supported by structural field evidence found in five dikes. In addition, based on the plunge of K(max), two mantle sources could be inferred; one of them which fed about 80% of the swarm would be located in the southern part of the region, and the other underlied the Valeria quarry. However, for all dikes the AARM tensors are not coaxial with AMS fabrics and show a magnetic lineation (AARM(max)) oriented to N30-60E, suggesting that magnetite grains were rotated clockwise from dike plane. The orientation of AARM lineation is similar to the orientation of a system of faults in which the Salvador normal fault is the most important. These faults were formed during Cretaceous rifting in the Reconcavo-Tucano-jatoba assemblage that corresponds to an aborted intra-continental rift formed during the opening of the South Atlantic. Therefore, the AARM fabric found for the Salvador dikes is probably tectonic in origin and suggests that the dike swarm was affected by the important tectonic event responsible for the break-up of the Gondwanaland. (C) 2008 Elsevier B.V. All rights reserved.

Inferring Contagion in Regulatory Networks

Several gene regulatory network models containing concepts of directionality at the edges have been proposed. However, only a few reports have an interpretable definition of directionality. Here, differently from the standard causality concept defined by Pearl, we introduce the concept of contagion in order to infer directionality at the edges, i.e., asymmetries in gene expression dependences of regulatory networks. Moreover, we present a bootstrap algorithm in order to test the contagion concept. This technique was applied in simulated data and, also, in an actual large sample of biological data. Literature review has confirmed some genes identified by contagion as actually belonging to the TP53 pathway.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Improved likelihood inference in Birnbaum-Saunders regressions

The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. Our simulation results suggest that the likelihood ratio test tends to be liberal when the sample size is small. We obtain a correction factor which reduces the size distortion of the test. Also, we consider a parametric bootstrap scheme to obtain improved critical values and improved p-values for the likelihood ratio test. The numerical results show that the modified tests are more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application. (C) 2009 Elsevier B.V. All rights reserved.

Modifications and Alternatives to the Tests of Levene and Brown & Forsythe for Equality of Variances and Means

The usual tests to compare variances and means (e. g. Bartlett`s test and F-test) assume that the sample comes from a normal distribution. In addition, the test for equality of means requires the assumption of homogeneity of variances. In some situation those assumptions are not satisfied, hence we may face problems like excessive size and low power. In this paper, we describe two tests, namely the Levene`s test for equality of variances, which is robust under nonnormality; and the Brown and Forsythe`s test for equality of means. We also present some modifications of the Levene`s test and Brown and Forsythe`s test, proposed by different authors. We analyzed and applied one modified form of Brown and Forsythe`s test to a real data set. This test is a robust alternative under nonnormality, heteroscedasticity and also when the data set has influential observations. The equality of variance can be well tested by Levene`s test with centering at the sample median.

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-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.

Forecasting with Vector Nonlinear Time Series Models

This work concerns forecasting with vector nonlinear time series models when errorsare correlated. Point forecasts are numerically obtained using bootstrap methods andillustrated by two examples. Evaluation concentrates on studying forecast equality andencompassing. Nonlinear impulse responses are further considered and graphically sum-marized by highest density region. Finally, two macroeconomic data sets are used toillustrate our work. The forecasts from linear or nonlinear model could contribute usefulinformation absent in the forecasts form the other model.

Estrutura espacial e sazonal da avifauna e considerações sobre a conservação de aves aquáticas em uma área úmida no Rio Grande do Sul, Brasil

Mosaicos de áreas úmidas fornecem hábitats para uma ampla gama de espécies de aves, que raramente se distribuem uniformemente dentro das mesmas. O cenário mundial atual do estudo de aves em áreas úmidas deixa bem claro que as metodologias para estudos quantitativos de aves em áreas úmidas ainda estão sendo criadas ou aperfeiçoadas. O mosaico formado pelas áreas úmidas do Banhado dos Pachecos é de reconhecida importância para a conservação de aves aquáticas, constituindo-se numa área ideal para estudos da avifauna. A presente dissertação tem como objetivo avaliar a estrutura espacial e sazonal da avifauna do Banhado dos Pachecos, tecer considerações sobre a conservação das aves aquáticas sob uma perspectiva de paisagem e testar a viabilidade de se utilizar amostragens matinais e vespertinas para análises de distribuição e abundância da avifauna. O Banhado dos Pachecos, juntamente com o Banhado Grande, formam o Sistema Banhado Grande. A amostragem da avifauna foi conduzida através de levantamentos qualitativos e quantitativos de modo a cobrir quatro estações climáticas: verão, outono, inverno e primavera. As amostragens qualitativas foram realizadas através de deslocamentos ad libitum entre e durante as amostragens quantitativas em todas as fisionomias. As amostragens quantitativas foram realizadas através de pontos de contagem, transecções e contagens totais. Riqueza, grupos funcionais de forrageio, grupos funcionais de nidificação, aves aquáticas, situação de ocorrência no Rio Grande do Sul, espécies ameaçadas de extinção e abundância foram os descritores utilizados para a caracterização da avifauna. A estatística empregada na análise dos dados multivariados baseou-se em métodos não-paramétricos de reamostragem através de aleatorização e “bootstrap”. Análises de agrupamentos foram realizadas para determinar a formação de grupos de fisionomias e análises de coordenadas principais foram realizadas para determinar se existia algum padrão de associação entre as diferentes fisionomias. Registraram-se 209 espécies de aves, vinte e e três grupos funcionais de forrageio, sete grupos funcionais de nidificação e 60 espécies de aves aquáticas e 11 espécies ameaçadas de extinção. Trinta e duas espécies apresentaram evidências discordantes da situação de ocorrência conhecida para o estado. Alguns fatores que poderiam ser fontes de viés para a interpretação das análises na presente dissertação foram abordados. A constância encontrada no conjunto de espécies da área de estudo pode refletir uma maior estabilidade ambiental. O alto número de grupos funcionais de forrageio e de nidificação registrados para a área de estudo sugere uma grande diversidade de recursos, reflexo da heterogeneidade entre as diferentes fisionomias. A origem de algumas espécies que se mostraram efetivamente migratórias, pois usaram a área de estudo em um período estacional bem definido, se mostra uma incógnita. Somente estudos extensivos e abrangentes poderão responder essas perguntas e propor medidas eficientes para a conservação tanto das áreas úmidas como das espécies que delas dependem. A restauração de um corredor de áreas úmidas entre o banhado dos Pachecos e o banhado Grande, juntamente com um manejo rotativo de cultivos de arroz parece ser a alternativa mais viável e conciliatória entre pontos de vista econômico e conservacionista para possibilitar o aumento da conectividade no Sistema Banhado Grande.