Sampling design proportional to order statistic of auxiliary variable

The sampling designs dependent on sample moments of auxiliary variables are well known. Lahiri (Bull Int Stat Inst 33:133–140, 1951) considered a sampling design proportionate to a sample mean of an auxiliary variable. Sing and Srivastava (Biometrika 67(1):205–209, 1980) proposed the sampling design proportionate to a sample variance while Wywiał (J Indian Stat Assoc 37:73–87, 1999) a sampling design proportionate to a sample generalized variance of auxiliary variables. Some other sampling designs dependent on moments of an auxiliary variable were considered e.g. in Wywiał (Some contributions to multivariate methods in, survey sampling. Katowice University of Economics, Katowice, 2003a); Stat Transit 4(5):779–798, 2000) where accuracy of some sampling strategies were compared, too.These sampling designs cannot be useful in the case when there are some censored observations of the auxiliary variable. Moreover, they can be much too sensitive to outliers observations. In these cases the sampling design proportionate to the order statistic of an auxiliary variable can be more useful. That is why such an unequal probability sampling design is proposed here. Its particular cases as well as its conditional version are considered, too. The sampling scheme implementing this sampling design is proposed. The inclusion probabilities of the first and second orders were evaluated. The well known Horvitz–Thompson estimator is taken into account. A ratio estimator dependent on an order statistic is constructed. It is similar to the well known ratio estimator based on the population and sample means. Moreover, it is an unbiased estimator of the population mean when the sample is drawn according to the proposed sampling design dependent on the appropriate order statistic.     

Open spaces for dialogue promoting mental health as a social work education methodology

ABSTRACT

The authors discuss service user involvement as a key approach regarding training of social workers. In many European Union countries this is a stable practice with a lengthy tradition in research and application. However, in Poland it is almost entirely absent and marginalized. This article presents the results of a participatory action research project conducted at the Institute of Sociology of the Jagiellonian University in Krakow, the objective of which was to identify and critically analyze the key substantive and formal aspects of training of social workers with the participation of individuals with experience of mental illness. This research project adopted an open approach to cognizing reality based on qualitative co-participatory methods. In the conclusion, the authors emphasize that the fundamental criterion for the success of this particular form of training is voluntary and differentiated participation of students—both in the role of people sharing their own experience and as learners—as well as shaping a culture of open dialogue, educational alliances of recognition and recovery, the foundation of which is axiological experience.     

Discriminant coordinates analysis for multivariate functional data

Abstract

One of the basic statistical methods of dimensionality reduction is analysis of discriminant coordinates given by Fisher (1936 Fisher, R. A. 1936. The use of multiple measurements in taxonomic problem. Annals of Eugenics 7 (2):179–88. doi:10.1111/j.1469-1809.1936.tb02137.x.[Crossref] , [Google Scholar]) and Rao (1948). The space of discriminant coordinates is a space convenient for presenting multidimensional data originating from multiple groups and for the use of various classification methods (methods of discriminant analysis). In the present paper, we adapt the classical discriminant coordinates analysis to multivariate functional data. The theory has been applied to analysis of textural properties of apples of six varieties, measured over a period of 180?days, stored in two types of refrigeration chamber.     

Recycling the orphan photograph: the new life of Jewish objects

The aim of this article is to explore the new lives of prewar photographs of European Jewry. In particular, I employ the concept of ‘orphan photograph’ which describes any work whose owners, producers, and the subjects featured in them are no longer available. Working from the premise that a photograph is not only a two-dimensional representation but also a three-dimensional object, I show how family images are consumed, distributed, discarded, salvaged and brought back to life. As I argue in this article, with the annihilation of their owners the once-important personal meanings of the pictures become obscured and obliterated. Subsequently, in post-Holocaust culture orphan photographs become invested with collective values. In the process of being recycled, these private family photographs are transformed into public spaces through which new visions of the past are projected and group interests promoted. Drawing on two case studies from Poland, I look at the ways in which these orphaned images are used by writers and NGOs, and examine how the various agents affect the subsequent readings of these artefacts. The article shows that once allowed to ‘speak for themselves’ these images reveal an immense capacity to challenge our pre-set notions of the past and escape the ‘backshadowing’ narrative of the Shoah.     

Recruitment and Retention of Latinos in Social Work Education: Building on Students’ Community Cultural Wealth

Spanish-speaking and culturally sensitive social workers are in high demand throughout the country to work with Latino clients. Latinos currently represent about 11% of active social workers, limiting the capacity of social work to effectively address the needs of the Latino population. Despite this shortage, little attention has been paid to the recruitment and retention of Latinos in social work. This article presents a case study that examines a BSW program accredited by the Council on Social Work Education, at a bilingual, private college where 90% of students self-identify as Latinos. It details how the BSW program builds on the students’ community cultural wealth to ensure continued recruitment and retention of Latino students. Implications for social work education are discussed.     

An Automatic Test for the Umbrella Alternatives

The paper proposes a new test for detecting the umbrella pattern under a general non‐parametric scheme. The alternative asserts that the umbrella ordering holds while the hypothesis is its complement. The main focus is put on controlling the power function of the test outside the alternative. As a result, the asymptotic error of the first kind of the constructed solution is smaller than or equal to the fixed significance level α on the whole set where the umbrella ordering does not hold. Also, under finite sample sizes, this error is controlled to a satisfactory extent. A simulation study shows, among other things, that the new test improves upon the solution widely recommended in the literature of the subject. A routine, written in R, is attached as the Supporting Information file.     

New bounds for locally irregular chromatic index of bipartite and subcubic graphs

A graph is locally irregular if the neighbors of every vertex v have degrees distinct from the degree of v. A locally irregular edge-coloring of a graph G is an (improper) edge-coloring such that the graph induced on the edges of any color class is locally irregular. It is conjectured that three colors suffice for a locally irregular edge-coloring. In the paper, we develop a method using which we prove four colors are enough for a locally irregular edge-coloring of any subcubic graph admiting such a coloring. We believe that our method can be further extended to prove the tight bound of three colors for such graphs. Furthermore, using a combination of existing results, we present an improvement of the bounds for bipartite graphs and general graphs, setting the best upper bounds to 7 and 220, respectively.     

Development of urban behaviour is associated with time since urbanization in a reed-nesting waterbird

Behavioural adaptations are recognized as crucial determinants for successful establishment and persistence of animal populations in a novel urban environment. Here, we examined mechanisms responsible for the development of urban behavioural type in a common waterbird, the Eurasian coot Fulica atra. We compared the behaviour of coots from a rural population and two urban populations that differed in the timing of colonization event (1960s vs. 2000s). We found that some behavioural characters associated with urban life (aggression during nest defence and boldness towards humans during foraging) were more strongly expressed in the older urban population when compared with the recently established urban population. By contrast, coots from the two urban populations showed a similar likelihood of exploiting human-derived food resources, as well as they showed similar levels of physiological stress. Urban coots were generally more aggressive, bolder, and less stressed than their rural conspecifics. Large behavioural and physiological divergence of coots from the recently established urban population and their rural conspecifics suggested that phenotypic plasticity and phenotype sorting may play a key role in the initial stages of urban colonization. On the other hand, increasing expression of boldness and aggression with the time since urbanization may suggest the role of microevolutionary adaptation in response to novel selective forces associated with the urban environment. Our results indicate that a combination of different processes (phenotypic plasticity, phenotype sorting, and microevolution) can determine successful colonization of urban areas by the Eurasian coots, and possibly other bird species.     

Asymptotic behaviour of proportions of observations in random regions determined by central order statistics from stationary processes

In this paper, we show that proportions of observations that fall into a random region determined by a given Borel set and a central order statistic converge almost surely, provided that the corresponding population quantile is unique. We also describe three types of possible asymptotic behaviour of these proportions in the case of non-unique population quantile. As an application of our findings we establish limiting properties of numbers of ties with a central order statistics in a discrete sample. Our results are derived not only for independent and identically distributed observations but more generally for strictly stationary and ergodic sequences of random variables.