Order statistics from overlapping samples: bivariate densities and regression properties

In this paper, we are interested in the joint distribution of two order statistics from overlapping samples. We give an explicit formula for the distribution of such a pair of random variables under the assumption that the parent distribution is absolutely continuous. We are also interested in the question to what extent conditional expectation of one of such order statistic given another determines the parent distribution. In particular, we provide a new characterization by linearity of regression of an order statistic from the extended sample given the one from the original sample, special case of which solves a problem explicitly stated in the literature. It appears that to describe the correct parent distribution it is convenient to use quantile density functions. In several other cases of regressions of order statistics we provide new results regarding uniqueness of the distribution in the sample.     

On a problem with singularity in comparison of linear experiments

For consistency, the parameter space in the Gauss-Markov model with singular covariance matrix is usually restricted by observation vector. This restriction arises some difficulties in comparison of linear experiments. To avoid it we reduce the problem of comparison from singular to nonsingular case.     

Women on strike: mobilizing against reproductive injustice in Poland

The paper employs a lens of reproductive justice (RJ) to discuss the events of the 2016 mobilization against a total abortion ban proposal in Poland. By presenting the context of women’s rights in Poland, especially the abortion debates, we argue that the 2016 Women’s Strike showed that taking a stand for reproductive justice was countered by governmental actions. By using a case study approach, the paper analyzes the Strike as a tumultuous act of women’s solidarity while simultaneously assessing its implications for RJ issues. We discuss the aftermath and the socio-political reticence to acknowledge the complexities of women’s lives and reproductive choices. Further, we provide arguments for applying the RJ framework into discerning the notion of ideal citizens and gendered social control in Poland. This localized analysis has a global relevance by reflecting the impact of worldwide trends in women’s rights activism and RJ in the context of resurfacing nationalisms and populism.     

An association between bone mineral density and anabolic hormones in middle-aged and elderly men with prediabetes

Introduction: Prediabetes (PD) leads to reduced testosterone (T) in males, but the association between the anabolic hormones and bone mineral density (BMD) remains unknown.

Objectives: We investigated an association between the anabolic hormones and BMD in middle-aged and elderly men with PD.

Methods: We investigated 84 prediabetic and 56 control men. Total T (TT), calculated free T (cFT), and dehydroepiandrosterone sulfate (DHEAS) were measured, and BMD was assessed using DXA methods.

Results: Patients with PD had lower TT (p?p?<?.005), and DHEAS (p?<?.02) than control group. BMD values of the lower lumbar spine (p?<?.02) and total body (p?<?.05) in prediabetic men were lower than in control group. Lumbar spine BMD correlated with TT (r?=?0.376), cFT (r?=?0.235), and HbA1c (r?=??0.368); femoral neck BMD correlated with TT (r?=?0.412) and cFT (r?=?0.421). The high lumbar spine and femur neck BMD was associated with high TT, cFT, and low HbA1c, while the high total body BMD with high TT, cFT, and low HbA1c.

Conclusion: The anabolic hormones significantly affect BMD in male with PD, and screening for low BMD is necessary in these patients.     

The Polish Social Enterprise Sector Vis-à-Vis the Welfare Regime: Following on the Solidarity Movement?

This paper presents the development of the enterprise sector and the welfare regime in Poland, dominated by two opposing trends originating from the country’s recent history: remnants of the “Communist welfare state” and liberal tendencies that came after the political and economic transformation in 1989. The growing civil society that supplements a deficient welfare system finds its roots in the peaceful underground Solidarity movement of the 1980s which played a great role in liberating Poland. After the political turnover, the Solidarity’s mission-driven approach not only survived, but also helped shape Poland’s contemporary civil society. The outlined mechanisms seem to be significant for understanding the transformation of social economy and the welfare state concept in post-communist Europe. In our paper, we identify six mechanisms underlying the Solidarity movement, which, when subsequently implemented by social entrepreneurs, has guaranteed the success of their organizations. We will also characterize the current welfare state in Poland, as well as the role of social enterprises in filling the gaps and addressing the shortcomings of the welfare state. Several case studies will illustrate the latter.     

Comparison of dispersions of mixtures of ordered distributions

In the paper we consider mixtures of unknown stochastically ordered distribution functions according to known mixing distribution functions. We provide optimal lower and upper bounds on ratios of general dispersion measures of such mixtures. The bounds do not depend on the particular form of dispersion measure. We present applications of the results in reliability theory, insurance mathematics, Bayesian statistics, and regression analysis.     

Does Consumer Confidence Forecast Household Saving and Borrowing Behavior? Evidence for Poland

Consumer confidence plays an important role in households’ decision-making processes. This study investigates the effects of consumer confidence on household saving and borrowing behavior that are unsatisfactorily considered in previous discussions. The questions of interest are first, whether indexes of consumer confidence have any predictive power on their own for future household saving and borrowing rates, and second, whether they contain information about future household saving and borrowing rates aside from the information contained in other available indicators. In addition to aggregate confidence indicators, their components are used to provide more precise information. Overall, the multiple linear regression analysis (OLS technique) of Polish time-series data gives positive answers to both questions. This finding supports the recommendation of combining the strengths of objective indicators (such as economic fundamentals) and subjective indicators (such as consumer confidence) to improve household financial behavior forecasts.     

The “ugly” face of social investment? The politics of childcare in Central and Eastern Europe

In this article, we aim to understand the development dynamics of a specific area of social investment (SI), that is, childcare policies, in the context of postcommunist politics and the recent right-wing turn that took place in the Czech Republic, Hungary, and Poland. This article identifies varieties of channels for promoting SI. First, in taking the perspective of the “mixed economy of welfare,” we argue that attempts made to introduce elements of SI to the childcare policies involved various leading roles available for either the private sector or state/public domain. Second, it is important to distinguish between implicit/unintended and explicit/intended projects both in relation to cases in which SI strategy is applied via marketization/privatization and when it involves a government-led project. Third, we take into account the politics of SI implementation that might involve applying certain principles central to policy concepts (such as “investment”) in justifying policy instruments incompatible with original ideas. Although arguments about SI have been extensively used by Eastern European leaders, their goal has been to justify welfare reforms that were implicitly or explicitly directed towards the middle class while excluding the “nondeserving” often based on ethnic identity. We characterize Poland as a case of “implicit marketization,” the Czech Republic as a case of “explicit privatization,” and the Hungarian version of SI as a case of “explicit public dualization.” In this, we show that in some cases, the implementation of SI approaches by right-wing populist parties might rear its “ugly” head.     

Some properties of the generalized TTT transform

Recently Li and Shaked [2007. A general family of univariate stochastic orders. J. Statist. Plann. Inference 137, 3601–3610] introduced the generalized total time on test (GTTT) transform with respect to a given function ?$?$. In this paper we study some properties of it which are related with stochastic orderings. A concept of Lehmann and Rojo [1992. Invariant directional orderings. Ann. Statist. 20, 2100–2110] is applied to a new setting and the GTTT transform is used to define invariance properties and distances of some stochastic orders. Iterations of the GTTT transforms are also studied and their relations with exponential mixtures of gamma distributions are established.     

On MSE of EBLUP

We consider Best Linear Unbiased Predictors (BLUPs) and Empirical Best Linear Unbiased Predictors (EBLUPs) under the general mixed linear model. The BLUP was proposed by Henderson (Ann Math Stat 21:309–310, 1950). The formula of this BLUP includes unknown elements of the variance-covariance matrix of random variables. If the elements in the formula of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) are replaced by some type of estimators, we obtain the two-stage predictor called the EBLUP which is model-unbiased (Kackar and Harville in Commun Stat A 10:1249–1261, 1981). Kackar and Harville (J Am Stat Assoc 79:853–862, 1984) show an approximation of the mean square error (the MSE) of the predictor and propose an estimator of the MSE. The MSE and estimators of the MSE are also studied by Prasad and Rao (J Am Stat Assoc 85:163–171, 1990), Datta and Lahiri (Stat Sin 10:613–627, 2000) and Das et al. (Ann Stat 32(2):818–840, 2004). In the paper we consider the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976. Ża̧dło (On unbiasedness of some EBLU predictor. Physica-Verlag, Heidelberg, pp 2019–2026, 2004) shows that the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) may be treated as a generalisation of the BLUP proposed by Henderson (Ann Math Stat 21:309–310, 1950) and proves model unbiasedness of the EBLUP based on the formula of the BLUP proposed by Royall (J Am Stat Assoc 71:657–473, 1976) under some assumptions. In this paper we derive the formula of the approximate MSE of the EBLUP and its estimators. We prove that the approximation of the MSE is accurate to terms o(D ⁻¹) and that the estimator of the MSE is approximately unbiased in the sense that its bias is o(D ⁻¹) under some assumptions, where D is the number of domains. The proof is based on the results obtained by Datta and Lahiri (Stat Sin 10:613–627, 2000). Using our results we show some EBLUP based on the special case of the general linear model. We also present the formula of its MSE and estimators of its MSE and their performance in Monte Carlo simulation study.