Interval censored and truncated data: Rate of convergence of NPMLE of the density

We consider survival data that are both interval censored and truncated. Under appropriate assumptions on the involved distributions, the censoring, truncation and survival, we prove the consistency of the NPMLE of the density of the survival, and give the rate of convergence. Finally, we give an example where the joint law of the censoring and truncation can be explicitly computed.     

Is ethnic prejudice declining in Britain? Change in social distance attitudes among ethnic majority and minority Britons

Most literature on racial prejudice deals with the racial attitudes of the ethnic majority and ethnic minorities separately. This paper breaks this tradition. We examine the social distance attitudes of white and non‐white British residents to test if these attitudes follow the same trends over time, whether they are driven by the same social processes and whether they are inter‐related. We have three main findings. Firstly, social distance from other ethnic groups has declined over time for both white and ethnic minority Britons. For the white majority there are both period and cohort elements to this decline. Secondly, we see some evidence that social distance between the majority and minority groups is reciprocal. Specifically, minorities who experience rejection by the white British feel a greater sense of distance from them. Thirdly, we find that all groups share the perception of the same ethnic hierarchy. We see evidence of particularly widespread hostility towards Muslim Britons from all ethnic groups suggesting that Muslims are singled out for negative attention from many British residents of all other backgrounds, including a large number who do not express hostility to other groups.     

On Old-Fashioned Versus Modern Homonegativity Distinction: Evidence From Poland

Psychological research on prejudice against homosexuals distinguishes between old-fashioned (traditional) and modern (contemporary) homonegativity, which differ with regard to their content, correlates, and consequences. The current research offers evidence for the validity of old-fashioned versus modern homonegativity distinction in the post-communist, East European context. In Studies 1 and 2 (Ns = 295 and 327, respectively) the Polish adaptations of the non-gendered and gendered Homonegativity Scale (Morrison, Parriag, & Morrison, 1999) and the Modern Homonegativity Scale (Morrison & Morrison, 2003) were developed. Furthermore, divergent (discriminant) validity of traditional and contemporary anti-homosexual prejudice was demonstrated. Old-fashioned and modern homonegativity exhibited differential relationships with social distance and support for same-sex couples’ relational rights.     

Thinking through tragedy: critical distance and the law of genre

Abstract

This article focuses on two problems associated with tragedy. One ancient: what is it that draws us to the dramatic presentation of events of terrible suffering and loss? And one modern: namely, that while tragedies are still performed and appreciated, little new tragedy is being written. It will be argued in relation to the second problem that the vitality of tragedy as a dramatic form requires a less rigid approach to what might be considered tragic. And in relation to the first problem it will be argued that this more expansive conception of tragedy will allow an understanding of the ‘pay-off’ of tragedy in a way that draws both on the tradition that focuses on tragedy as cathartic therapeutic, and on the tradition that sees it as a thought laboratory that allows ethical dilemmas to be posed and explored from different perspectives. This argument constitutes a two-fold dialectical synthesis (emotional and intellectual approaches to tragedy on the one hand and the technical and popular use of the word ‘tragedy’ on the other) and the effect of this is to facilitate an understanding of tragedy as establishing a ‘critical distance’ that sets the scene for the possibility of thinking.     

Merging data from multiple sources: pretest and shrinkage perspectives

In this article, we have developed asymptotic theory for the simultaneous estimation of the k means of arbitrary populations under the common mean hypothesis and further assuming that corresponding population variances are unknown and unequal. The unrestricted estimator, the Graybill-Deal-type restricted estimator, the preliminary test, and the Stein-type shrinkage estimators are suggested. A large sample test statistic is also proposed as a pretest for testing the common mean hypothesis. Under the sequence of local alternatives and squared error loss, we have compared the asymptotic properties of the estimators by means of asymptotic distributional quadratic bias and risk. Comprehensive Monte-Carlo simulation experiments were conducted to study the relative risk performance of the estimators with reference to the unrestricted estimator in finite samples. Two real-data examples are also furnished to illustrate the application of the suggested estimation strategies.     

New goodness of fit tests for the Cauchy distribution

Some goodness-of-fit procedures for the Cauchy distribution are presented. The power comparisons indicate that the new tests possess good performances among the competitors, especially against symmetric alternatives. A financial data set is analyzed for illustration.     

Empirical Uncertain Bayes Methods in Area‐level Models

Random effects model can account for the lack of fitting a regression model and increase precision of estimating area‐level means. However, in case that the synthetic mean provides accurate estimates, the prior distribution may inflate an estimation error. Thus, it is desirable to consider the uncertain prior distribution, which is expressed as the mixture of a one‐point distribution and a proper prior distribution. In this paper, we develop an empirical Bayes approach for estimating area‐level means, using the uncertain prior distribution in the context of a natural exponential family, which we call the empirical uncertain Bayes (EUB) method. The regression model considered in this paper includes the Poisson‐gamma and the binomial‐beta, and the normal‐normal (Fay–Herriot) model, which are typically used in small area estimation. We obtain the estimators of hyperparameters based on the marginal likelihood by using a well‐known expectation‐maximization algorithm and propose the EUB estimators of area means. For risk evaluation of the EUB estimator, we derive a second‐order unbiased estimator of a conditional mean squared error by using some techniques of numerical calculation. Through simulation studies and real data applications, we evaluate a performance of the EUB estimator and compare it with the usual empirical Bayes estimator.     

Optimum designs for parameter estimation in a mixture experiment with two correlated responses

In this paper, we investigate a mixture problem with two responses, which are functions of the mixing proportions, and are correlated with known dispersion matrix. We obtain D- and A-optimal designs for estimating the parameters of the response functions, when none or some of the regression coefficients of the two functions are the same. It is shown that when no prior knowledge about the regression coefficients is available, the D-optimal design is independent of the dispersion matrix, while the A-optimal design depends on it, provided the response functions are of different degree. On the other hand, when some of the regression coefficients are known to be the same for both the functions, the D-optimal design depends on the dispersion matrix when the two response functions are not of the same degree.     

Generalized minimum aberration mixed-level orthogonal arrays: A general approach based on sequential integer quadratically constrained quadratic programming

Orthogonal fractional factorial designs and in particular orthogonal arrays (OAs) are frequently used in many fields of application, including medicine, engineering, and agriculture. In this article, we present a methodology and an algorithm to find an OA, of given size and strength, which satisfies the generalized minimum aberration criterion. The methodology is based on the joint use of polynomial counting functions, complex coding of levels, and algorithms for quadratic optimization and puts no restriction on the number of levels of each factor.     

Schematic saturated orthogonal arrays obtained by using the contractive replacement method

This paper presents a general method of constructing schematic saturated orthogonal arrays of strength two. We consider a class of mixed saturated orthogonal arrays produced from saturated symmetric orthogonal arrays by using the contractive replacement method, study the Hamming distances of the rows, construct their association schemes, and prove that they are schematic. Some examples are given to illustrate this construction method.