On nonlinear multi-covering problems

In this paper we define the exact k-coverage problem, and study it for the special cases of intervals and circular-arcs. Given a set system consisting of a ground set of n points with integer demands \(\{d_0,\dots ,d_{n-1}\}\) and integer rewards, subsets of points, and an integer k, select up to k subsets such that the sum of rewards of the covered points is maximized, where point i is covered if exactly \(d_i\) subsets containing it are selected. Here we study this problem and some related optimization problems. We prove that the exact k-coverage problem with unbounded demands is NP-hard even for intervals on the real line and unit rewards. Our NP-hardness proof uses instances where some of the natural parameters of the problem are unbounded (each of these parameters is linear in the number of points). We show that this property is essential, as if we restrict (at least) one of these parameters to be a constant, then the problem is polynomial time solvable. Our polynomial time algorithms are given for various generalizations of the problem (in the setting where one of the parameters is a constant).     

Reinvigorating the social contract and strengthening social cohesion: Social protection responses to COVID-19

The COVID-19 pandemic has exposed the vulnerability of those who are inadequately covered by social protection in more and less developed countries alike, and has exacerbated the fragility of a social contract that was already under strain in many countries. A weak social contract in the context of an exceptional crisis poses a very real risk to social cohesion. Nevertheless, many States have reasserted themselves as the guarantor of rights by protecting public health and incomes. By sustaining these measures, economic recovery will be supported which will help minimize risks that may weaken social cohesion. However, this is a fast-moving, inherently unstable and protracted crisis. Social protection stands at a critical juncture. Decisive policy action will be required to strengthen social protection systems, including floors, as one of the cornerstones of a reinvigorated social contract.     

Distribution-free test for symmetry based on Bonferroni's measure

We propose a test based on Bonferroni's measure of skewness. The test detects the asymmetry of a distribution function about an unknown median. We study the asymptotic distribution of the given test statistic and provide a consistent estimate of its variance. The asymptotic relative efficiency of the proposed test is computed along with Monte Carlo estimates of its power. This allows us to perform a comparison of the test based on Bonferroni's measure with other tests for symmetry.     

Zero variance Markov chain Monte Carlo for Bayesian estimators

Interest is in evaluating, by Markov chain Monte Carlo (MCMC) simulation, the expected value of a function with respect to a, possibly unnormalized, probability distribution. A general purpose variance reduction technique for the MCMC estimator, based on the zero-variance principle introduced in the physics literature, is proposed. Conditions for asymptotic unbiasedness of the zero-variance estimator are derived. A central limit theorem is also proved under regularity conditions. The potential of the idea is illustrated with real applications to probit, logit and GARCH Bayesian models. For all these models, a central limit theorem and unbiasedness for the zero-variance estimator are proved (see the supplementary material available on-line).     

Point estimation after early stopping in a repeated measures trial

When the individual measurements are statistically independent, the maximum likelihood estimator calculated at the end of a sequential procedure overestimates the underlying effect. There are many clinical trials in which we are interested in comparing changes in responses between two treatment groups sequentially. Lee and DeMets (1991, JASA 86, 757–762) proposed a group sequential method for comparing rates of change when a response variable is measured for eaeh patient at successive follow-up visits. They assumed that the response follows the linear mixed effects model and derived the asymptotic joint distribution of the sequentially computed statistics. In this article, we consider the maximum likelihood estimator (MLE), the median unbiased estimator (MUE) and the midpoint of a 100(1-α)% confidence interval as point estimators for the rate of change in the linear mixed effects model, and investigate their properties by Monte Carlo simulation.     

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

This paper proposes a new nested algorithm (NPL) for the estimation of a class of discrete Markov decision models and studies its statistical and computational properties. Our method is based on a representation of the solution of the dynamic programming problem in the space of conditional choice probabilities. When the NPL algorithm is initialized with consistent nonparametric estimates of conditional choice probabilities, successive iterations return a sequence of estimators of the structural parameters which we call K–stage policy iteration estimators. We show that the sequence includes as extreme cases a Hotz–Miller estimator (for K=1) and Rust's nested fixed point estimator (in the limit when K→∞). Furthermore, the asymptotic distribution of all the estimators in the sequence is the same and equal to that of the maximum likelihood estimator. We illustrate the performance of our method with several examples based on Rust's bus replacement model. Monte Carlo experiments reveal a trade–off between finite sample precision and computational cost in the sequence of policy iteration estimators.     

Perceived Aspects of Home Environment and Home Modifications by Older People Living in Rural Areas

This study investigated the relationships between the “perceived aspects” of current home environment of elderly people living in rural areas and their home modification behavior. To investigate this perception, home satisfaction, perception of home capability, and home safety were used as perceived aspects of the home. Data were collected by a questionnaire. The response rate was 43.1%, with 317 eligible questionnaires. The results from this study indicate that there was no significant difference in perceived aspects of home environment between those who modified their homes and those who did not. Regardless of their current home conditions, most elderly respondents (75%) showed high home satisfaction. Results from this study suggest that a modified home environment does not necessarily contribute to an older person's perception of perceived aspects of their home environment.     

Kompetenzen als Auswahlbasis von Coaches

Many companies are increasingly making use of coaching as an instrument of human resources development. The selection of the a suitable coach is more often based on intuition of the selecting human resources employees than it is objective. This underscores the need for a more systematic approach to the selection of coaches, which is based on the useable competencies of a coach and is also scientifically supported. Through a multiparadigm literature review and an explorative study, this article identifies seven base competencies of coaches, which can serve as a foundation for the selection of a coach.     

Several biplot methods applied to gene expression data

DNA microarray experiments result in enormous amount of data, which need careful interpretation. Biplot approaches show simultaneous display of genes and samples in low-dimensional graphs and thus can be used to represent the relationships between genes and samples. There are several different types of biplots, and these methods need to be evaluated because each plot provides different result.     

Social care and support for elderly men and women in an urban and a rural area of Nepal

This study has aimed to describe the care and support for urban and rural elderly people of Bhaktapur district, Nepal. Efforts were made to identify the feeling of some features of general well-beings associated to mental health, person responsible for care and support, capability to perform daily routine activities, sources of finance and ownership to the property. More than half of the respondents were found having single or multiple features of loneliness, anxiety, depression and insomnia. The rate of point prevalence loneliness was found higher in the above 80 years of age, urban respondents. Almost 9 in 10 respondents were capable themselves to dress, walk and maintain personal hygiene and majority of them were assisted by spouse, son/daughter-in-laws. Family support was common sources of income and ownership to the property was absolutely high.