Deconvolution for an atomic distribution: rates of convergence

Let $X_1,..., X_n$ be i.i.d.\ copies of a random variable $X=Y+Z,$ where $X_i=Y_i+Z_i,$ and $Y_i$ and $Z_i$ are independent and have the same distribution as $Y$ and $Z,$ respectively. Assume that the random variables $Y_i$'s are unobservable and that $Y=AV,$ where $A$ and $V$ are independent, $A$ has a Bernoulli distribution with probability of success equal to $1-p$ and $V$ has a distribution function $F$ with density $f.$ Let the random variable $Z$ have a known distribution with density $k.$ Based on a sample $X_1,...,X_n,$ we consider the problem of nonparametric estimation of the density $f$ and the probability $p.$ Our estimators of $f$ and $p$ are constructed via Fourier inversion and kernel smoothing. We derive their convergence rates over suitable functional classes. By establishing in a number of cases the lower bounds for estimation of $f$ and $p$ we show that our estimators are rate-optimal in these cases.Comment: 27 page

n\sqrt{n}-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing

We consider the problem of parameter estimation for a system of ordinary differential equations from noisy observations on a solution of the system. In case the system is nonlinear, as it typically is in practical applications, an analytic solution to it usually does not exist. Consequently, straightforward estimation methods like the ordinary least squares method depend on repetitive use of numerical integration in order to determine the solution of the system for each of the parameter values considered, and to find subsequently the parameter estimate that minimises the objective function. This induces a huge computational load to such estimation methods. We study the consistency of an alternative estimator that is defined as a minimiser of an appropriate distance between a nonparametrically estimated derivative of the solution and the right-hand side of the system applied to a nonparametrically estimated solution. This smooth and match estimator (SME) bypasses numerical integration altogether and reduces the amount of computational time drastically compared to ordinary least squares. Moreover, we show that under suitable regularity conditions this smooth and match estimation procedure leads to a $\sqrt{n}$-consistent estimator of the parameter of interest.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ362 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

How do perceived changes in inequality affect health?

Individuals do not possess an entirely accurate assessment of the level of income differences in their society and so changes in quantitative measures of income inequality may not always align with changes in the perceptions of income inequality. This disconnect is partly driven by how people form their opinions about the level of inequality. In this study we explore whether there is an association between perceptions of inequality and health, and if so, how it differs depending on the specific channel through which people formed their opinions about changes in income inequality. Drawing on data from 31 European and Eurasian countries, we find that both men and women are more likely to report bad health when their perceptions of increasing inequality are formed through experiences of inequality in their communities than through media and other channels

Intergenerational Social Mobility and Popular Explanations of Poverty: A Comparative Perspective

This article explores the consequences of intergenerational social mobility on perceptions of popular explanations of poverty. It is hypothesised that those who experience improvements in socio-economic status through social mobility are more likely to blame poverty on individual characteristics such as laziness and lack of willpower and are less likely to attribute failure to injustice in society, and on the macro-level, the effect of social mobility on perceptions of popular explanations of poverty is moderated by contextual environment. The described hypotheses are tested by using multinomial and multilevel logistic regressions and two complementary datasets—European Values Studies and the Life in Transition Survey. The derived findings suggest that social mobility is indeed associated with perceptions of individual blame and social blame of why some people are in need. However, these effects are manifested primarily among subjectively mobile individuals and are also conditioned by the legacy of socialism and the level of economic development of countries where individuals reside

Mortality in Transition: Study Protocol of the PrivMort Project, a multilevel convenience cohort study

Background: Previous research using routine data identified rapid mass privatisation as an important driver of mortality crisis following the collapse of Communism in Central and Eastern Europe. However, existing studies on the mortality crisis relying on individual level or routine data cannot assess both distal (societal) and proximal (individual) causes of mortality simultaneously. The aim of the PrivMort Project is to overcome these limitations and to investigate the role of societal factors (particularly rapid mass privatisation) and individual-level factors (e.g. alcohol consumption) in the mortality changes in post-communist countries. Methods: The PrivMort conducts large-sample surveys in Russia, Belarus and Hungary. The approach is unique in comparing towns that have undergone rapid privatisation of their key industrial enterprises with those that experienced more gradual forms of privatisation, employing a multi-level retrospective cohort design that combines data on the industrial characteristics of the towns, socio-economic descriptions of the communities, settlement-level data, individual socio-economic characteristics, and individuals’ health behaviour. It then incorporates data on mortality of different types of relatives of survey respondents, employing a retrospective demographic approach, which enables linkage of historical patterns of mortality to exposures, based on experiences of family members. By May 2016, 63,073 respondents provided information on themselves and 205,607 relatives, of whom 102,971 had died. The settlement-level dataset contains information on 539 settlements and 12,082 enterprises in these settlements in Russia, 96 settlements and 271 enterprises in Belarus, and 52 settlement and 148 enterprises in Hungary. Discussion: In addition to reinforcing existing evidence linking smoking, hazardous drinking and unemployment to mortality, the PrivMort dataset will investigate the variation in transition experiences for individual respondents and their families across settlements characterized by differing contextual factors, including industrial characteristi

The effect of rapid privatisation on mortality in mono-industrial towns in post-Soviet Russia: a retrospective cohort study

Background Population-level data suggest that economic disruptions in the early 1990s increased working-age male mortality in post-Soviet countries. This study uses individual-level data, using an indirect estimation method, to test the hypothesis that fast privatisation increased mortality in Russia. Methods In this retrospective cohort study, we surveyed surviving relatives of individuals who lived through the post-communist transition to retrieve demographic and socioeconomic characteristics of their parents, siblings, and male partners. The survey was done within the framework of the European Research Council (ERC) project PrivMort (The Impact of Privatization on the Mortality Crisis in Eastern Europe). We surveyed relatives in 20 mono-industrial towns in the European part of Russia (ie, the landmass to the west of the Urals). We compared ten fast-privatised and ten slow-privatised towns selected using propensity score matching. In the selected towns, population surveys were done in which respondents provided information about vital status, sociodemographic and socioeconomic characteristics and health-related behaviours of their parents, two eldest siblings (if eligible), and first husbands or long-term partners. We calculated indirect age-standardised mortality rates in fast and slow privatised towns and then, in multivariate analyses, calculated Poisson proportional incidence rate ratios to estimate the effect of rapid privatisation on all-cause mortality risk. Findings Between November, 2014, and March, 2015, 21 494 households were identified in 20 towns. Overall, 13 932 valid interviews were done (with information collected for 38 339 relatives [21 634 men and 16 705 women]). Fast privatisation was strongly associated with higher working-age male mortality rates both between 1992 and 1998 (age-standardised mortality ratio in men aged 20–69 years in fast vs slow privatised towns: 1·13, SMR 0·83, 95% CI 0·77–0·88 vs 0·73, 0·69–0·77, respectively) and from 1999 to 2006 (1·15, 0·91, 0·86–0·97 vs 0·79, 0·75–0·84). After adjusting for age, marital status, material deprivation history, smoking, drinking and socioeconomic status, workingage men in fast-privatised towns experienced 13% higher mortality than in slow-privatised towns (95% CI 1–26). Interpretation The rapid pace of privatisation was a significant factor in the marked increase in working-age male mortality in post-Soviet Russia. By providing compelling evidence in support of the health benefits of a slower pace of privatisation, this study can assist policy makers in making informed decisions about the speed and scope of government interventions

Parental transmission of smoking among middle-aged and older populations in Russia and Belarus

Objectives The very high rates of smoking among men and the rapid changes among women in the Post-Soviet countries mean that this region offers an opportunity to understand better the intergenerational role of parental influences on smoking. Methods In this study, we exploit a unique data set, the PrivMort cohort study conducted in 30 Russian and 20 Belarusian towns in 2014–2015, which collects information on behaviours of middle-aged and older individuals and their parents, including smoking. We explored the associations between smoking by parents and their offspring using multiply imputed data sets and multilevel mixed-effect Poisson regressions. Results Adjusting for a wide array of social origin, socio-demographic, and socio-economic variables, our analysis suggests that sons of regularly smoking fathers have prevalence ratios of 1.35 [95% confidence intervals (CI) 1.21–1.50] and 1.39 (CI 1.23–1.58) of smoking, while the figures for daughters of regularly smoking mothers are 1.91 (CI 1.40–2.61) and 2.30 (CI 1.61–3.28), respectively, in Russia and Belarus. Conclusions Intergenerational paternal and maternal influences on smoking should be taken into account in studies seeking to monitor the rates of smoking and the impact of tobacco control programme

Intergenerational mobility in relative educational attainment and health-related behaviours

Research on intergenerational social mobility and health-related behaviours yields mixed fndings. Depending on the direction of mobility and the type of mechanisms involved, we can expect positive or negative association between intergenerational mobility and health-related behaviours. Using data from a retrospective cohort study, conducted in more than 100 towns across Belarus, Hungary and Russia, we ft multilevel mixed-efects Poisson regressions with two measures of health-related behaviours: binge drinking and smoking. The main explanatory variable, intergenerational educational mobility is operationalised in terms of relative intergenerational educational trajectories based on the prevalence of specifed qualifcations in parental and ofspring generations. In each country the associations between intergenerational educational mobility, binge drinking and smoking was examined with incidence rate ratios and predicted probabilities, using multiply imputed dataset for missing data and controlling for important confounders of healthrelated behaviours. We fnd that intergenerational mobility in relative educational attainment has varying association with binge drinking and smoking and the strength and direction of these efects depend on the country of analysis, the mode of mobility, the gender of respondents and the type of health-related behaviour. Along with accumulation and Falling from Grace hypotheses of the consequences of intergenerational mobility, our fndings suggest that upward educational mobility in certain instances might be linked to improved health-related behaviours

Equality of opportunity is linked to lower mortality in Europe

Background: This study investigates if intergenerational equality of opportunity is linked to mortality in 30 European countries. Equality of opportunity may lead to greater returns on health investments and, consequently, improved health outcomes. In turn, a perceived lack of fairness in the distribution of life chances and limited possibilities for upward intergenerational mobility can cause anxiety among individuals and gradually compromise their health. Methods: We used information on 163 467 individuals' and their parents' Socio-Economic Index of Occupational Status from a large survey data set-the European Social Survey-to generate three complementary measures of equality of opportunity. We then linked these to administrative data on total, gender-specific and cause-specific mortality rates assembled by Eurostat from the national statistical offices. Results: We found that lower equality of opportunity, measured by the attainment of individuals from the lowest and highest quartiles of socioeconomic status and by the overall intergenerational correlation in socioeconomic status, was related to higher mortality rates, particularly in relation to diseases of the nervous system and the sense organs, diseases of the respiratory system and external causes of mortality. Our measures of equality of opportunity were more consistently linked with mortality of men than women. Conclusion: Equality of opportunity may be an important explanation of mortality that warrants further research. Measures that aim at facilitating intergenerational social mobility can be justified not only via normative considerations of equality of opportunity but also in terms of individuals' chances to enjoy healthy lives