Computing Probabilities of Type I Error and Type II Error of Sequential Bayesian Procedures for Testing One-Sided Hypotheses

In this article, it is shown how to compute, in an approximated way, probabilities of Type I error and Type II error of sequential Bayesian procedures for testing one-sided null hypotheses. First, some theoretical results are obtained, and then an algorithm is developed for applying these results. The prior predictive density plays a central role in this study.     

Inferences for Mixtures of Distributions for Centrally Censored Data with Partial Identification

In this article, several methods to make inferences about the parameters of a finite mixture of distributions in the context of centrally censored data with partial identification are revised. These methods are an adaptation of the work in Contreras-Cristán, Gutiérrez-Peña, and O'Reilly (2003 Contreras-Cristán , A. , Gutiérrez-Peña , E. , O'Reilly , F. ( 2003 ). Inferences using latent variables for mixtures of distributions for censored data with partial identification . Comm. Stat. Theor. Meth. 32 ( 4 ): 749 – 774 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) in the case of right censoring. The first method focuses on an asymptotic approximation to a suitably simplified likelihood using some latent quantities; the second method is based on the expectation-maximization (EM) algorithm. Both methods make explicit use of latent variables and provide computationally efficient procedures compared to non-Bayesian methods that deal directly with the full likelihood of the mixture appealing to its asymptotic approximation. The third method, from a Bayesian perspective, uses data augmentation to work with an uncensored sample. This last method is related to a recently proposed Bayesian method in Baker, Mengersen, and Davis (2005 Baker , P. , Mengersen , K. , Davis , G. ( 2005 ). A Bayesian solution to reconstructing centrally censored distributions . J. Agr. Biol. Environ. Stat. 1 : 61 – 84 . [Google Scholar]). Our proposal of the three adapted methods is shown to provide similar inferential answers, thus offering alternative analyses.     

The Alpha-power Tobit Model

The main object of this article is to propose an extension of the tobit model for which the error distribution follows the power-normal distribution (Gupta and Gupta, 2008 Gupta , D. , Gupta , R. C. ( 2008 ). Analyzing skewed data by power normal model . Test 17 : 197 – 210 .[Crossref], [Web of Science ®] , [Google Scholar]). Inference is dealt with by using the likelihood approach. Simulation studies and application to a real data set are used to demonstrate the usefulness of the extension.     

Estimating additive models with missing responses

ABSTRACT

For multivariate regressors, the Nadaraya–Watson regression estimator suffers from the well-known curse of dimensionality. Additive models overcome this drawback. To estimate the additive components, it is usually assumed that we observe all the data. However, in many applied statistical analysis missing data occur. In this paper, we study the effect of missing responses on the additive components estimation. The estimators are based on marginal integration adapted to the missing situation. The proposed estimators turn out to be consistent under mild assumptions. A simulation study allows to compare the behavior of our procedures, under different scenarios.     

A method for estimating lorenz curves

This paper proposes a new method for estimating the parameters of Lorenz Curves (LC’s) and fitting LC’s to observed data. The method is very general. It is applicable to any family of LC’s as long as it is given in closed form which is often the case in practice. The method can also be applied to either the LC or to its associated distribution. The estimators are easy to compute as they are obtained one at a time by solving only one equation in one unknown and in many cases the solutions are given in closed-forms. An additional advantage, that is not shared with the currently used method of estimation, is that the method is invariant as to the specification of which variable is written as a function of the other in the LC form. The method is applied to the most commonly suggested LC’s families. An example of real-life data is used to illustrate the methodology. A simulation study is performed to study the properties of the proposed estimators and to compare them with existing ones. The results seem to indicate that the proposed estimators have good properties and they often perform much better than the existing ones.     

On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization

This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is “matched” to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.     

Fluid adaptation of contested citizenship: second-generation migrant Turks in Germany and the United States

This paper explores belonging in the context of legal citizenship for second-generation Turkish immigrants in Berlin and in New York. Fluid adaptation refers to the discursive boundaries of immigrant identity articulations, the contextual and shifting adjustments immigrants make to their sense of belonging. Immigrant belonging, gauged by ‘encounters’ with bureaucracies and participatory expressions, is shaped in large part by the receiving state's legal framework and citizenship status. Belonging is complicated by racialization and exclusion, and affected by intersectionalities of immigrant experience. Limited citizenship models necessitate deployment of fluid and alternative membership models. Alternative forms of belonging underscore the power of the nation-state in delimiting belonging.     

Determinants of mortality transition in developing countries before and after the Second World War: Some evidence from Cuba

Few studies provide an insight into what factors contributed to declines in the mortality rates of developing countries before the Second World War. In this paper, statistics on causes of death from Cuba, particularly Havana, are used to investigate what may have been some of the principal determinants of mortality decline in the developing world before the arrival of modern drugs and insecticides. Trends in cause-specific mortality are examined in the light of Cuba's social, economic, medical and public health history. The Cuban experience strongly suggests that in this country public health and sanitary reforms and nutritional improvements were largely responsible for initial declines in mortality throughout the first half of the twentieth century. One important finding is that the impact of these reforms and improved nutrition was greatly influenced by prevailing economic conditions. Periods of economic prosperity facilitated declines in mortality; but in times of adversity, the reverse occurred. It appears that during prosperous periods the maintenance and expansion of public health and sanitary facilities were made possible by increased public and private revenues, and that individuals had access to a more abundant diet. The severe economic crisis of the Great Depression had the opposite effect. With the appearance of sulphonamides in the late 1930s, antibiotics, and residual insecticides and other specific measures at the end of the Second World War, the relevance of economic conditions as a determinant of mortality decline diminished. Although this analysis points to the aforementioned trends, the Cuban experience also suggests that other factors enter into the process of declining mortality and that this phenomenon can only be explained as the result of the complex interplay of many forces.     

A New Proposal to Gauge Intergenerational Mobility: Educational Mobility in Europe as a Case Study

This paper is aimed at presenting a new intergenerational mobility index that (a) combines the intergenerational elasticity and the R-squared of the intergenerational regression and (b) enables the expression of the total degree of mobility as the weighted sum of mobility with respect to both parents. As a case study, we apply our proposal to investigate the intergenerational mobility of education in several European countries and its changes across birth cohorts. The results derived from the proposed index indicate that Nordic countries display higher levels of educational mobility than Southern countries, whereas continental countries are in an intermediate position. Moreover, it appears that the degree of mobility increases over time only in those countries with low initial levels and remains stable for the most mobile countries. Finally, for most of the countries the proposed methodology can prove that the degree of educational mobility with respect to each parent tends to converge to the same level over the course of time.