Consistency of non parametric estimators of the area under the ROC curve

ABSTRACT

The area under the receiver operating characteristic (ROC) curve is a popular summary index that measures the accuracy of a continuous-scale diagnostic test to measure its accuracy. Under certain conditions on estimators of distribution functions, we prove a theorem on strong consistency of the non parametric “plugin” estimators of the area under the ROC curve. Based on this theorem, we construct some new “plugin” consistent estimators. The performance of the non parametric estimators considered is illustrated numerically and the estimators are compared in terms of bias, variance, and mean square error.     

On Vervaat and Vervaat-error-type processes for partial sums and renewals

We study the asymptotic behaviour of stochastic processes that are generated by sums of partial sums of i.i.d. random variables and their renewals. We conclude that these processes cannot converge weakly to any nondegenerate random element of the space D[0,1]$D[0,1]$. On the other hand, we show that their properly normalized integrals as Vervaat-type stochastic processes converge weakly to a squared Wiener process. Moreover, we also deal with the asymptotic behaviour of the deviations of these processes, the so-called Vervaat-error-type processes.     

Trapped in migrants’ sectors? Polish women in the Icelandic labour market

The employment‐driven migrations from Poland to Iceland have largely been pioneered by Polish women. They outnumbered men among Polish residents in this country until the economic boom since 2005 triggered large‐scale male immigration. This trend slowed down with the outbreak of the financial crisis, as the recession severely affected the male‐dominated construction industry. The analysis of Polish female migrants’ working experiences shows that recent inflows are mainly shaped by the nature of labour demand as well as the social policies and care services in Iceland. Although economically integrated, compared with native women Polish women tend to occupy rather disadvantaged positions. They seem concentrated in a few low‐skilled occupations that bring little prestige and low income. On the other hand, they were less affected by the financial crisis, in the sense that many of them maintained work, though some experienced lowering of salaries or reduction of working hours.     

Approximation of the Fisher price index by using the Lloyd–Moulton index: Simulation study

The Lloyd–Moulton price index does not make use of current-period expenditure data and, as it is commonly known, it allows us to approximate superlative indices, in particular the Fisher price index. This is a very important property for the inflation measurement and the Consumer Price Index bias calculations. In this article, we verify the utility of the Lloyd–Moulton price index in the Fisher price index approximation. We propose a simple modification of that index which reduces the variation of the estimator of an unknown parameter in this index formula. We also examine the influence of the price volatility on the quality of estimation of the parameter from the Lloyd–Moulton formula.     

Bounds for the expected value of the stochastic Divisia's price index

In this article, we estimate bounds for the expected value of the stochastic Divisia's price index, that is, we assume that prices and quantities of the given commodities are stochastic processes with continuous time. We consider some special case of the stochastic model in which prices and quantities are described by the geometric Brownian motion. It is shown that the precision of this estimation depends rather on the volatility of prices than quantities volatilities.     

Hard Times! How do Households Cope with Financial Difficulties? Evidence from the Swiss Household Panel

This study investigates impact of debt arrears and various consequential compensatory actions on self-reported satisfaction with life and the financial situation. The link between financial difficulties and the responses they demand has rarely been translated into satisfaction measures in the past. This study informs the literature about actual consequences of problems with arrears and impact of different coping strategies on household satisfaction measures. To address the questions at hand, data from the six (2010–2015) waves of the Swiss Household Panel were examined. A panel data model with fixed effects estimator was applied to account for unobserved population heterogeneity and mitigate the issues of omitted variables. The study confirmed that severe debt problems disproportionally affected self-reported satisfaction measures. Responses to arrears, if representing likely long-term solutions, did not signify further deterioration in self-reported measures. However, if arrears required resort to bank credit, disposal of household valuables or borrowing from family and friends, satisfaction with the household financial situation and household head life satisfaction were likely to suffer more.     

Emigration of Poles to the United Kingdom: history,present state and future prospects

The history of Polish immigration within the United Kingdom is several centuries old. Yet never in its history was such a mass migration as that after the Polish accession to the EU in 2004. During the over ten years that followed, almost a million Poles chose to settle in the United Kingdom. This article reviews and analyses past and present Polish emigration to the United Kingdom. It provides answers to questions regarding who the Polish immigrants are, what work they perform and how they have integrated within British society. It also considers the factors that have influenced the future dynamics of migration from Poland. Based on these, we have formed the hypothesis that while the years of 2004‐2016 saw, statistically, the largest emigration from Poland to the United Kingdom in recorded history, in the future, the number of Polish expatriates living in the United Kingdom will drop or at least the number of newcomers will decrease.     

The effect of dance therapy on the balance of women over 60 years of age: The influence of dance therapy for the elderly

Dance therapy is a physical activity that can lead to balance improvement in older adults. The aim of the study was to evaluate the effects of dance therapy on balance and risk of falls in older women. Twenty-four older women (mean age 66.4 years old) attended dance sessions for three months. Pretest/posttests were completed using the Postural Stability Test, the Limits of Stability Test, and the Fall Risk Test M-CTSIB. Results showed the Limits of Stability Test was significantly higher (17.5%) after dance classes. Regular use of dance therapy shows promise in improving balance by increasing the limits of stability.     

Some notes on poisson limits for empirical point processes

The authors define the scaled empirical point process. They obtain the weak limit of these point processes through a novel use of a dimension‐free method based on the convergence of compensators of multiparameter martingales. The method extends previous results in several directions. They obtain limits at points where the density may be zero, but has regular variation. The joint limit of the empirical process evaluated at distinct points is given by independent Poisson processes. They provide applications both to nearest‐neighbour density estimation in high dimensions, and to the asymptotic behaviour of multivariate extremes such as those arising from bivariate normal copulas. The Canadian Journal of Statistics 37: 347–360; 2009 © 2009 Statistical Society of Canada