A sequence of improved standard errors under heteroskedasticity of unknown form

The linear regression model is commonly used by practitioners to model the relationship between the variable of interest and a set of explanatory variables. The assumption that all error variances are the same (homoskedasticity) is oftentimes violated. Consistent regression standard errors can be computed using the heteroskedasticity-consistent covariance matrix estimator proposed by White (1980). Such standard errors, however, typically display nonnegligible systematic errors in finite samples, especially under leveraged data. Cribari-Neto et al. (2000) improved upon the White estimator by defining a sequence of bias-adjusted estimators with increasing accuracy. In this paper, we improve upon their main result by defining an alternative sequence of adjusted estimators whose biases vanish at a much faster rate. Hypothesis testing inference is also addressed. An empirical illustration is presented.     

Measuring the Cultural Dimension of Migrant Integration and Integration Policy in the European Context: Dilemmas and Discussions1

Migrant integration is usually studied in four dimensions: economic, political, social and cultural. The cultural sphere seems to be the most ambiguous, but also the one that induces various interpretations as it touches upon core norms and values held both by migrants and by the receiving society. This paper aims to reconstruct research approaches to cultural integration and integration policy. Beside the receiving country’s language, that is the obvious differentiating factor of cultural integration, other aspects have been defined: migrants’ religion, knowledge of the receiving country’s symbolic culture, maintenance and transmission of cultural patterns, cultural identity. Furthermore, indicators which appear to adequately measure the effectiveness of integration activities have been assigned to the predefined aspects of cultural integration. They have been confronted with indicators used within integration policies of selected EU states and with expert statements (collected within the Delphi method‐based survey) on given aspects of policies aimed at cultural integration.     

Histogram estimation of radon-nikodym derivatives for strong mixing data

Nonparametric inference for point processes is discussed by way of histograms, which provide a nice tool for the analysis of on-line data. The construction of histograms depends on a sequence of partitions, which we take tc be nonenibedded to allow partitions with sets of equal measure. This presents some theoretical problems, which are addressed with an assumption on the decomposition of second order moments. In another direction, we drop the usual independence assumption on the sample, replacing it by a strong mixing assumption. Under this setting, we study the convergence of the histogram in probability, which depends on approximation conditions between the distributions of random pairs and the product of their marginal distributions, and^almost completely, which is based on the decomposition of the second order moments. This last convergence is stated on two versions according to the assumption of Laplace transforms or the Cramer moment conditions. These are somewhat stronger, but enable us to recover the usual condition on the decrease rate of sets on each partition. In the final section we prove that the finite dimensional distributions converge in distribution to a Gaussian centered vector with a specified covariance.     

Power Law Selection Model for Repairable Systems

A repairable system, under minimal repair, is usually modeled according to a Non-Homogeneous Poisson Process (NHPP) assuming a Power Law intensity function. A traditional approach considers iid NHPPs in order to conduct a statistical analysis based on a sample of systems. However, systems might be heterogeneous due to unmeasured variables such as age, suppliers, and so on. In order to verify this assumption a frequentist approach is proposed in this article. Some possible model scenarios considering different systems heterogeneity are compared using likelihood ratio tests and information criteria. Real data sets illustrate the proposed methodology.     

Alternative estimator for the parameters of a mixture of two binomial distributions

The method of moments has been widely used as a simple alternative to the maximum likelihood method, mainly because of its efficiency and simplicity in obtaining parameter estimators of a mixture of two binomial distributions. In this paper, an alternative estimate is proposed which is as competitive as of the method of moments when comparing the mean squared error and computational effort.     

Life Satisfaction in Brazil: Testing the Psychometric Properties of the Satisfaction With Life Scale (SWLS) in Five Brazilian Samples

The aim of this paper was to validate the Brazilian-Portuguese version of the Satisfaction With Life Scale (SWLS), presenting evidence of its reliability and construct and criterion-related validity. A large Brazilian sample (2,180 participants), from five different populations (undergraduate and high school students, general population, elementary school teachers, and physicians), was considered. The results confirmed the single factorial structure and reliability (0.77 < Cronbach’s α < 0.88, mean α = 0.81) of the SWLS. Supporting its criterion-related validity, the SWLS correlated positively with positive affect and negatively with both negative affect and psychological distress across all five samples. The findings indicate that the Brazilian-Portuguese version of the SWLS is a valid instrument to use with diverse Brazilian samples.     

Point and block prediction in log-Gaussian random fields: The non-constant mean case

This work considers the problems of point and block prediction in log-Gaussian random fields for the case when the mean of the log-process is not constant and depends linearly on unknown parameters. First, we propose a new point predictor that is optimal within a certain family of predictors, which extend a result in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] that holds in the case when the mean of the log-process is constant. Second, we show that the results in De Oliveira [2006. On optimal point and block prediction in log-Gaussian random fields. Scand. J. Statist. 33, 523–540.] regarding optimal block prediction cannot be extended to the case when the mean of the log-process is not constant. Specifically, we show that the two families of block predictors considered by De Oliveira lack an optimal predictor. Finally, we numerically compare the predictive efficiency of the proposed point and block predictors.     

Log-Weibull extended regression model: Estimation,sensitivity and residual analysis

The failure rate function commonly has a bathtub shape in practice. In this paper we discuss a regression model considering new Weibull extended distribution developed by Xie et al. (2002) that can be used to model this type of failure rate function. Assuming censored data, we discuss parameter estimation: maximum likelihood method and a Bayesian approach where Gibbs algorithms along with Metropolis steps are used to obtain the posterior summaries of interest. We derive the appropriate matrices for assessing the local influence on the parameter estimates under different perturbation schemes, and we also present some ways to perform global influence. Also, some discussions on case deletion influence diagnostics are developed for the joint posterior distribution based on the Kullback–Leibler divergence. Besides, for different parameter settings, sample sizes and censoring percentages, are performed various simulations and display and compare the empirical distribution of the Martingale-type residual with the standard normal distribution. These studies suggest that the residual analysis usually performed in normal linear regression models can be straightforwardly extended to the martingale-type residual in log-Weibull extended models with censored data. Finally, we analyze a real data set under a log-Weibull extended regression model. We perform diagnostic analysis and model check based on the martingale-type residual to select an appropriate model.