A survey on multivariate chi-square distributions and their applications in testing multiple hypotheses

We are concerned with three different types of multivariate chi-square distributions. Their members play important roles as limiting distributions of vectors of test statistics in several applications of multiple hypotheses testing. We explain these applications and consider the computation of multiplicity-adjusted p-values under the respective global hypothesis. By means of numerical examples, we demonstrate how much gain in level exhaustion or, equivalently, power can be achieved with corresponding multivariate multiple tests compared with approaches which are only based on univariate marginal distributions and do not take the dependence structure among the test statistics into account. As a further contribution of independent value, we provide an overview of essentially all analytic formulas for computing multivariate chi-square probabilities of the considered types which are available up to present. These formulas were scattered in the previous literature and are presented here in a unified manner.     

Stationary bootstrapping for panel cointegration tests under cross-sectional dependence

Stationary bootstrapping is applied to panel cointegration tests which are based on the ordinary least-squares estimator and the seemingly unrelated regression (SUR) estimator of the residual unit root. Large sample validity of stationary bootstrapping is established. A finite sample experiment reveals that size performances of the bootstrap tests are much less sensitive to cross-sectional correlation than those of existing tests and a test based on the SUR estimator has substantially better power than existing tests.     

Threshold‐free estimation of functional antibody titers of a group B streptococcus opsonophagocytic killing assay

Opsonophagocytic killing assays (OPKA) are routinely used for the quantification of bactericidal antibodies in blood serum samples. Quantification of the OPKA readout, the titer, provides the basis for the statistical analysis of vaccine clinical trials having functional immune response endpoints. Traditional OPKA titers are defined as the maximum serum dilution yielding a predefined bacterial killing threshold value, and they are estimated by fitting a dose‐response model to the dilution‐killing curve. This paper illustrates a novel definition of titer, the threshold‐free titer, which preserves biological interpretability while not depending on any killing threshold or on a postulated shape of the dose‐response curve. These titers are shown to be more precise than the traditional threshold‐based titers when using simulated and experimental group B streptococcus OPKA experimental data. Also, titer linearity is shown to be not measurable when using threshold‐based titers, whereas it becomes measurable using threshold‐free titers. The biological interpretability and operational characteristics demonstrated here indicate that threshold‐free titers are an appropriate tool for the routine analysis of OPKA data. Copyright © 2015 John Wiley & Sons, Ltd.     

A Bayesian estimate of the concordance correlation coefficient with skewed data

Concordance correlation coefficient (CCC) is one of the most popular scaled indices used to evaluate agreement. Most commonly, it is used under the assumption that data is normally distributed. This assumption, however, does not apply to skewed data sets. While methods for the estimation of the CCC of skewed data sets have been introduced and studied, the Bayesian approach and its comparison with the previous methods has been lacking. In this study, we propose a Bayesian method for the estimation of the CCC of skewed data sets and compare it with the best method previously investigated. The proposed method has certain advantages. It tends to outperform the best method studied before when the variation of the data is mainly from the random subject effect instead of error. Furthermore, it allows for greater flexibility in application by enabling incorporation of missing data, confounding covariates, and replications, which was not considered previously. The superiority of this new approach is demonstrated using simulation as well as real‐life biomarker data sets used in an electroencephalography clinical study. The implementation of the Bayesian method is accessible through the Comprehensive R Archive Network. Copyright © 2015 John Wiley & Sons, Ltd.     

Relative Risk Regression for Binary Outcomes: Methods and Recommendations

Relative risks are often considered preferable to odds ratios for quantifying the association between a predictor and a binary outcome. Relative risk regression is an alternative to logistic regression where the parameters are relative risks rather than odds ratios. It uses a log link binomial generalised linear model, or log‐binomial model, which requires parameter constraints to prevent probabilities from exceeding 1. This leads to numerical problems with standard approaches for finding the maximum likelihood estimate (MLE), such as Fisher scoring, and has motivated various non‐MLE approaches. In this paper we discuss the roles of the MLE and its main competitors for relative risk regression. It is argued that reliable alternatives to Fisher scoring mean that numerical issues are no longer a motivation for non‐MLE methods. Nonetheless, non‐MLE methods may be worthwhile for other reasons and we evaluate this possibility for alternatives within a class of quasi‐likelihood methods. The MLE obtained using a reliable computational method is recommended, but this approach requires bootstrapping when estimates are on the parameter space boundary. If convenience is paramount, then quasi‐likelihood estimation can be a good alternative, although parameter constraints may be violated. Sensitivity to model misspecification and outliers is also discussed along with recommendations and priorities for future research.     

Hedging Barrier Options in GARCH Models with Transaction Costs

This study proposes a modified strike‐spread method for hedging barrier options in generalized autoregressive conditional heteroskedasticity (GARCH) models with transaction costs. A simulation study was conducted to investigate the hedging performance of the proposed method in comparison with several well‐known static methods for hedging barrier options. An accurate, easy‐to‐implement and fast scheme for generating the first passage time under the GARCH framework which enhances the accuracy and efficiency of the simulation is also proposed. Simulation results and an empirical study using real data indicate that the proposed approach has a promising performance for hedging barrier options in GARCH models when transaction costs are taken into consideration.     

Approximating moments of continuous functions of random variables using Bernstein polynomials

Bernstein polynomials have many interesting properties. In statistics, they were mainly used to estimate density functions and regression relationships. The main objective of this paper is to promote further use of Bernstein polynomials in statistics. This includes (1) providing a high-level approximation of the moments of a continuous function $g\left(X\right)$ of a random variable $X$, and (2) proving Jensen’s inequality concerning a convex function without requiring second differentiability of the function. The approximation in (1) is demonstrated to be quite superior to the delta method, which is used to approximate the variance of $g\left(X\right)$ with the added assumption of differentiability of the function. Two numerical examples are given to illustrate the application of the proposed methodology in (1).     

The reinvention of the Promised Land: utopian space and time in Soviet Jewish exodus literature

The Jewish underground movement in the Soviet Union in the second half of the 1960s produced literature that became a part of the counterculture of Soviet dissent. For the first time in decades, Russian Jews identified, to a significant degree, as people of the galut (Jewish Diaspora). The battle for the return to Israel and the new Jewish renaissance in the intellectual sphere of the unofficial led to the emergence of new topographical concepts, which were inspired primarily by the Jewish cultural tradition. In fact, the exodus texts written in the 1960s–1980s represented a new, late Soviet shaping of Zionist prose. They relate to the symbol of the Promised Land as a fundamental projection of aspirations. Late Soviet Zionist texts share the traditional Jewish vision of Israel as an imagined topos of the original homeland that is both retrospective (with reference to the biblical promise of the land and the seizure of Canaan) and prospective (return and redemption). The Exodus story contained in Sefer Shemot becomes a leading poetic, philosophical and at times religiously charged metaphor of liberation and reunification. The re-strengthened collective memory of tradition required biblical symbols to be imbued with new semiotic power.

This paper will show that the historical dimension of the events dealt with in the literature often has strong mystical and mythological traits and displays messianic-apocalyptic hopes of salvation. However, alternative literary space and time models represented in the aliyah literature hereby betray their rootedness in the teleology of the communist regime. The powerful Israel utopia reflects both the eschatological time of the Soviet empire and its phantasms of paradise on earth. Late Soviet Zionism and totalitarian discourse are shown to be two space-time utopias.     

SafetiPin: an innovative mobile app to collect data on women's safety in Indian cities

Women's safety is a key concern of governments and civil society today. In India, the issue has become prominent in the wake of the gang rape and murder in 2012. One of the key elements in addressing the lack of safety in cities is identifying the causes. SafetiPin, a mobile app, is one tool that has been developed to collect data on safety in cities. Building on the international methodology of safety audits, SafetiPin has transformed it into a mobile app that crowd sources data and information on insecurity in cities. Using SafetiPin, data have been collected in seven Indian cities. This article examines some of the data to understand what factors lead to lack of safety and insecurity in cities, and discusses future plans for the project.     

Using repeated-prevalence data in multi-state modeling of renal replacement therapy

Multi-state models help predict future numbers of patients requiring specific treatments but these models require exhaustive incidence data. Deriving reliable predictions from repeated-prevalence data would be helpful. A new method to model the number of patients that switch between therapeutic modalities using repeated-prevalence data is presented and illustrated. The parameters and goodness of fit obtained with the new method and repeated-prevalence data were compared to those obtained with the classical method and incidence data. The multi-state model parameters’ confidence intervals obtained with annually collected repeated-prevalence data were wider than those obtained with incidence data and six out of nine pairs of confidence intervals did not overlap. However, most parameters were of the same order of magnitude and the predicted patient distributions among various renal replacement therapies were similar regardless of the type of data used. In the absence of incidence data, a multi-state model can still be successfully built with annually collected repeated-prevalence data to predict the numbers of patients requiring specific treatments. This modeling technique can be extended to other chronic diseases.