A Turning Point in Gender Bias in Mortality? An Update on the Number of Missing Women

Amartya Sen started a debate about gender bias in mortality by estimating the number of “missing women,” which refers to the number of females of any age who have presumably died as a result of discriminatory treatment. Depending on the assumptions made, the combined estimates for countries exhibiting the presence of such gender bias varied between 60 and 107 million. As new population data have become available for these countries, this article examines whether the number of “missing women” has changed in the past decade. The combined estimate of the number of missing women has risen in absolute terms but has fallen slightly in relation to overall population. Considerable improvement is evident in West Asia, North Africa, and parts of South Asia, while only small improvements have occurred in India and a deterioration took place in China. Analyses of the underlying causes of gender bias in mortality suggest that improvements are largely related to improved female education and employment opportunities and rising overall incomes, while deterioration is mostly attributable to the rising incidence of sex‐selective abortions.     

Mapping the Nomological Network of Career Self-Efficacy

This article examined the degree to which personality hardiness (control, commitment, and challenge), career beliefs (status, preference, motivation, and flexibility), self-efficacy (general and social), and occupational choice status related to career self-efficacy among a sample of 181 college juniors and seniors. Results from an intercorrelation matrix and regression analysis indicated that motivation, self-efficacy, occupational choice status, and commitment correlated significantly to career self-efficacy. Applications of these findings to career counseling are discussed.     

Small-Sample Comparisons for Goodness-of-Fit Statistics in One-Way Multinomials with Composite Hypotheses

The small-sample behaviour of power-divergence goodness-of-fit statistics with composite hypotheses was evaluated with multinomial models of up to five cells and up to three parameters. Their performance was assessed by comparing asymptotic test sizes with exact test sizes obtained by enumeration in the near right tail, where 1-?∈?(0.90,?0.95], and in the far right tail, where 1-?∈?(0.95,?0.99]. The study addressed all combinations of power-diparse JAS312HH01.sgmvergence estimates of indices ν?∈?{-1/2,?0,?1/3,?1/2,?2/3,?1,?3/ 2} and power-divergence statistics of indices λ?∈?{-1/2,?0,?1/3,?1/2,?2/3,?1,?3/2}. The results indicate that the asymptotic approximation is sufficiently accurate (by the criterion that the average exact size is no larger than ±10% of the nominal asymptotic test size) in the near right tail when ν=0 and λ=1/2, and in the far right tail when ν=0 and λ=1/3, in both cases providing that the smallest expectation in the composite hypothesis exceeds 5. The only exception to this rule is the case of models that render a near-equiprobable composite hypothesis on the boundaries of the parameter space, where average exact sizes are usually quite different from nominal sizes despite the fact that the smallest expectation in these conditions is usually well above 5.     

Comments on “The power of monitoring: how to make the most of a contaminated multivariate sample”

These are comments on the invited paper “The power of monitoring: How to make the most of a contaminated multivariate sample” by Andrea Cerioli, Marco Riani, Anthony Atkinson and Aldo Corbellini.     

Nonparametric validation of similar distributions and assessment of goodness of fit

In this paper the problem of assessing the similarity of two cumulative distribution functions F and G is considered. An asymptotic test based on an α-trimmed version of Mallows distance Γ_α( F , G ) between F and G is suggested, thus demonstrating the similarity of F and G within a preassigned Γ_α( F , G ) neighbourhood at a controlled type I error rate. The test proposed is applied to the validation of goodness of fit and for the nonparametric assessment of bioequivalence. It is shown that Γ_α( F , G ) can be interpreted as average and population equivalence. Our approach is illustrated by various examples.     

Small-sample comparisons for powerdivergence goodness-of-fit statistics for symmetric and skewed simple null hypotheses

Power-divergence goodness-of-fit statistics have asymptotically a chi-squared distribution. Asymptotic results may not apply in small-sample situations, and the exact significance of a goodness-of-fit statistic may potentially be over- or under-stated by the asymptotic distribution. Several correction terms have been proposed to improve the accuracy of the asymptotic distribution, but their performance has only been studied for the equiprobable case. We extend that research to skewed hypotheses. Results are presented for one-way multinomials involving k = 2 to 6 cells with sample sizes N = 20, 40, 60, 80 and 100 and nominal test sizes f = 0.1, 0.05, 0.01 and 0.001. Six power-divergence goodness-of-fit statistics were investigated, and five correction terms were included in the study. Our results show that skewness itself does not affect the accuracy of the asymptotic approximation, which depends only on the magnitude of the smallest expected frequency (whether this comes from a small sample with the equiprobable hypothesis or a large sample with a skewed hypothesis). Throughout the conditions of the study, the accuracy of the asymptotic distribution seems to be optimal for Pearson's X² statistic (the power-divergence statistic of index u = 1) when k > 3 and the smallest expected frequency is as low as between 0.1 and 1.5 (depending on the particular k, N and nominal test size), but a computationally inexpensive improvement can be obtained in these cases by using a moment-corrected h² distribution. If the smallest expected frequency is even smaller, a normal correction yields accurate tests through the log-likelihood-ratio statistic G² (the power-divergence statistic of index u = 0).     

Collinearity: revisiting the variance inflation factor in ridge regression

Ridge regression has been widely applied to estimate under collinearity by defining a class of estimators that are dependent on the parameter k. The variance inflation factor (VIF) is applied to detect the presence of collinearity and also as an objective method to obtain the value of k in ridge regression. Contrarily to the definition of the VIF, the expressions traditionally applied in ridge regression do not necessarily lead to values of VIFs equal to or greater than 1. This work presents an alternative expression to calculate the VIF in ridge regression that satisfies the aforementioned condition and also presents other interesting properties.     

Results of exploratory data analysis in the broken stick model

The broken stick model is a model of the abundance of species in a habitat, and it has been widely extended. In this paper, we present results from exploratory data analysis of this model. To obtain some of the statistics, we formulate the broken stick model as a probability distribution function based on the same model, and we provide an expression for the cumulative distribution function, which is needed to obtain the results from exploratory data analysis. The inequalities we present are useful in ecological studies that apply broken stick models. These results are also useful for testing the goodness of fit of the broken stick model as an alternative to the chi square test, which has often been the main test used. Therefore, these results may be used in several alternative and complementary ways for testing the goodness of fit of the broken stick model.     

Fitting three-dimensional Laguerre tessellations to foam structures

Foam models, especially random tessellations, are powerful tools to study the relations between the geometric structure of foams and their physical properties. In this paper, we propose the use of random Laguerre tessellations, weighted versions of the well-known Voronoi tessellations, as models for the microstructure of foams. Based on geometric characteristics estimated from a tomographic image of a closed-cell polymer foam, we fit a Laguerre tessellation model to the material. It is shown that this model allows for a better fit of the geometric structure of the foam than some classical Voronoi tessellation models.     

Linear calibration in functional regression models

This paper discusses calibration in functional regression models. Classical and inverse type estimators are considered. First order approximation to the bias and to the mean squared error (MSE) of the estimators are considered. Numerical comparisons seem to indicate that the classical estimator obtained via maximum likelihood estimation performs better than the other estimators considered.