The asymptotic distribution of numbers of observations near order statistics

In this paper, we discuss the limiting behavior of numbers of observations near an order statistic. We then derive an expression for the joint distribution of the numbers of observations that fall into the open right a-vicinity and left b-vicinity of k  th and (n-r)$(n-r)$th order statistics, respectively, from a sample of size n and establish the result that they are asymptotically independent under suitable conditions.     

Financial instruments used by Polish municipalities in response to the first wave of COVID-19

Public Organization Review - Studies on the influence of COVID-19 on municipalities are scarce, although it was precisely municipalities that stood in the first line of combat. It is important to...     

Extreme ranking analysis in robust ordinal regression

We extend the principle of robust ordinal regression with an analysis of extreme ranking results. In our proposal, we consider the whole set of instances of a preference model that is compatible with preference information provided by the DM. We refer to both, the well-known UTA^GMS method, which builds the set of general additive value functions compatible with DM's preferences, and newly introduced in this paper PROMETHEE^GKS, which constructs the set of compatible outranking models via robust ordinal regression. Then, we consider all complete rankings that follow the use of the compatible preference models, and we determine the best and the worst attained ranks for each alternative. In this way, we are able to assess its position in an overall ranking, and not only in terms of pairwise comparisons, as it is the case in original robust ordinal regression methods. Additionally, we analyze the ranges of possible comprehensive scores (values or net outranking flows). We also discuss extensions of the presented approach on other multiple criteria problems than ranking. Finally, we show how the presented methodology can be applied in practical decision support, reporting results of three illustrative studies.     

On Berry-Esseen theorem for some functions of U-statistics

The rate of convergence in the central limit theorem and in the random central limit theorem for some functions of U-statistics are established. The theorems refer to the asymptotic behaviour of the sequence {g(U_n),n≥1}, where g belongs to the class of all differentiable functions g such that g′εL(δ) and U_n is a U-statistics.     

Packing <Emphasis Type="Bold">[1, Δ]</Emphasis>-factors in graphs of small degree

Given an undirected, connected graph G with maximum degree Δ, we introduce the concept of a [1, Δ]-factor k-packing in G, defined as a set of k edge-disjoint subgraphs of G such that every vertex of G has an incident edge in at least one subgraph. The problem of deciding whether a graph admits a [1,Δ]-factor k-packing is shown to be solvable in linear time for k = 2, but NP-complete for all k≥ 3. For k = 2, the optimisation problem of minimising the total number of edges of the subgraphs of the packing is NP-hard even when restricted to subcubic planar graphs, but can in general be approximated within a factor of by reduction to the Maximum 2-Edge-Colorable Subgraph problem. Finally, we discuss implications of the obtained results for the problem of fault-tolerant guarding of a grid, which provides the main motivation for research.     

State of the art in U.S. multicultural social work practice: Client expectations and provider challenges

ABSTRACT

To obtain a comprehensive view of the level of knowledge and development achieved in multicultural social work practice, I conducted a scoping review of U.S. empirical literature for the 10-year period from 2007 through 2016. The review revealed that across the board racial and ethnic minority clients continue to experience marginalization and report low satisfaction with services. Conversely, providers are subject to some tensions and biases toward multicultural practice exacerbated by employers’ lack of emphasis on cultural competence. The problematic findings from the review suggest that our current approaches to cultural competence may need to be reexamined.     

Effects of human-related disturbance on breeding success of urban and non-urban blue tits (<Emphasis Type=Italic>Cyanistes caeruleus</Emphasis>)

There is a need to study the effects of urbanization on wildlife in order to understand the ecological implications of increasing urbanization and find out how to reduce its threats to biodiversity. The blue tit evolved as a forest species and prefers deciduous and mixed forests, whereas its nesting in urban habitats is a more recent phenomenon. Our long-term study of blue tit populations has been conducted in two habitats: an urban parkland (frequently visited by people) and a deciduous forest outside of the city. Using linear mixed modeling, we revealed that a relationship of blue tit breeding success (and the number of fledglings) with thermal conditions in May differed between the urban parkland and the forest. While the relationship was positive in the forest, it was negative in the parkland. In addition, breeding success in the parkland increased with increasing number of rainy days in May. We argue that the main possible reason for such patterns is human activity in the parkland, which interferes with tit parental care, especially the regular feeding of nestlings, whereas it is evidently associated with weather conditions. Human disturbance in the forest is likely to be negligible.     

Negative situation appraisal and mental well-being among refugees in Germany: Serial mediation by religious coping and sense of coherence

It has been widely demonstrated that pre- and post-migration experiences can be highly traumatic for refugees. The purpose of this study was to assess the mediating effects of religious coping and sense of coherence on the association of negative dysfunctional situation appraisal and mental well-being among refugees. Paper surveys were completed by 600 people representing various refugee groups (mostly from Mashreq Countries) in German Bavaria, aged 18–65. Mediation analysis revealed that negative religious coping and sense of coherence singly and serially mediated the relationship between negative dysfunctional situation appraisal and well-being, whereas positive religious coping did not have statistically significant relationships with these variables. The data obtained suggest that the negative religious coping style and sense of coherence are two important targets for future experimental studies, and interventions on them may bring the synergistic effect on improving mental well-being in refugees.     

Bounds on dispersion of order statistics based on dependent symmetrically distributed random variables

We consider a fixed number of arbitrarily dependent random variables with a common symmetric marginal distribution. For each order statistic based on the variables, we determine a common optimal bound, dependent in a simple way on the sample size and number of order statistics, for various measures of dispersion of the order statistics, expressed in terms of the same dispersion measure of the single original variable. The dispersion measures are connected with the notion of M-functional of a random variable location with respect to a symmetric and convex loss function. The measure is defined as the expected loss paid for the discrepancy between the M-functional and the variable. The most popular examples are the median absolute deviation and variance.