A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelation. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas–Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices of circulant type, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a CW(126, 64) and a CW(198, 100), whose existence was previously marked as unresolved in the most recent version of Strassler’s table.     

THE INFORMATION TECHNOLOGY REVOLUTION AND THE UNSECURED CREDIT MARKET

The information technology (IT) revolution coincided with the transformation of the U.S. unsecured credit market. Households' borrowing increased rapidly and there was an even faster increase in bankruptcy filings. A risk of default model with asymmetric information and costly screening is introduced to study this period. When information costs are high, the design of contracts under private information prevents some households from borrowing with a risk of default. As information costs drop, households borrow more and bankruptcy filings increase. Quantitative exercises suggest that the IT revolution may have played an important role in the transformation of the unsecured credit market. (JEL E43, E44, G33)     

‘What Was I Thinking?!’ Rhetorical Questions as a Technique to Identify and Explore Impasses in Therapy

Rhetorical questions emerging spontaneously in consultations can be used as a tool for developing self‐reflexivity and exploring the therapeutic alliance in the process of therapy with couples and families. This paper presents a technique based on the enunciation of rhetorical questions, which can point to an impasse in the process of therapy and contain a key to its resolution. The technique focuses on the distinctive feature of rhetorical questions as convening a paradoxical injunction: a question not intended as a question, while uttered as such. The technique in four steps is illustrated by examples from therapy, supervision, consultation, and self‐supervision. Its focus is the interlink between the therapeutic relationship and the process of therapy and it is informed by a second‐order cybernetics approach, dialogical practice, and the systemic literature on emotion. The technique can help develop curiosity in working with families, lead to unforeseen developments, and touch on prejudices not made explicit in previous therapeutic encounters. Whether we are acting as supervisors, therapists, or clients, the creation of a ‘secure enough’ context for rhetorical questions becomes critical to allow freeform exploration.     

A simple two-stage design for quantitative responses with application to a study in diabetic neuropathic pain

Two-stage designs offer substantial advantages for early phase II studies. The interim analysis following the first stage allows the study to be stopped for futility, or more positively, it might lead to early progression to the trials needed for late phase II and phase III. If the study is to continue to its second stage, then there is an opportunity for a revision of the total sample size. Two-stage designs have been implemented widely in oncology studies in which there is a single treatment arm and patient responses are binary. In this paper the case of two-arm comparative studies in which responses are quantitative is considered. This setting is common in therapeutic areas other than oncology. It will be assumed that observations are normally distributed, but that there is some doubt concerning their standard deviation, motivating the need for sample size review. The work reported has been motivated by a study in diabetic neuropathic pain, and the development of the design for that trial is described in detail.     

Link-tracing sampling with an initial sequential sample of sites: Estimating the size of a hidden human population

We proposed a modification to the variant of link-tracing sampling suggested by Félix-Medina and Thompson [M.H. Félix-Medina, S.K. Thompson, Combining cluster sampling and link-tracing sampling to estimate the size of hidden populations, Journal of Official Statistics 20 (2004) 19–38] that allows the researcher to have certain control of the final sample size, precision of the estimates or other characteristics of the sample that the researcher is interested in controlling. We achieve this goal by selecting an initial sequential sample of sites instead of an initial simple random sample of sites as those authors suggested. We estimate the population size by means of the maximum likelihood estimators suggested by the above-mentioned authors or by the Bayesian estimators proposed by Félix-Medina and Monjardin [M.H. Félix-Medina, P.E. Monjardin, Combining link-tracing sampling and cluster sampling to estimate the size of hidden populations: A Bayesian-assisted approach, Survey Methodology 32 (2006) 187–195]. Variances are estimated by means of jackknife and bootstrap estimators as well as by the delta estimators proposed in the two above-mentioned papers. Interval estimates of the population size are obtained by means of Wald and bootstrap confidence intervals. The results of an exploratory simulation study indicate good performance of the proposed sampling strategy.     

Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model

The distribution of the aggregate claims in one year plays an important role in Actuarial Statistics for computing, for example, insurance premiums when both the number and size of the claims must be implemented into the model. When the number of claims follows a Poisson distribution the aggregated distribution is called the compound Poisson distribution. In this article we assume that the claim size follows an exponential distribution and later we make an extensive study of this model by assuming a bidimensional prior distribution for the parameters of the Poisson and exponential distribution with marginal gamma. This study carries us to obtain expressions for net premiums, marginal and posterior distributions in terms of some well-known special functions used in statistics. Later, a Bayesian robustness study of this model is made. Bayesian robustness on bidimensional models was deeply treated in the 1990s, producing numerous results, but few applications dealing with this problem can be found in the literature.     

The t-information and its use in multivariate problems and time-series analysis

The second moment of recently introduced scalar inference function can be viewed as generalized Fisher information of the continuous probability distributions. In this paper we call it the t-information and give some possible applications of the new concept.     

Profile of the Present Slovak Society and its Regional Differences

The article is the first attempt in assessment of the development and the present situation of social structure and stratification in Slovakia. Its principal aim is to develop the profile of the present society in Slovakia, which reflects the pace and complexity of the transformation process and its impact on society. Processing of Micro census data from 2003 led to creation of the profile of society in Slovakia at the national level based on income distribution but also knowledge on regional societies and differences between them were obtained. It was found out that the present profile of the society in Slovakia is pear-shaped which means strong representation of lower strata and weaker representation of higher middle and high strata. The profile disclosed some specific features and inconsistencies in the present society of Slovakia, which were, and still are determined by many non standard past and present phenomena and processes often disguised by reforms. The information drawn in regions has facilitated identification of the basic nature and structure of regional societies, some of their specific features and negative elements and to demonstrate their highly differentiated character.

The importance of being mature: the effect of demographic maturation on global per capita GDP

Given that savings behaviour and worker productivity have strong life-cycle components and given that demographic profiles vary across countries, population age structure should be linked to differences in levels of economic development. In this paper, we measure the economic importance of age structure variation for the global economy. We find that demographic maturation has been associated with nearly half of the evolution of global per capita GDP since 1960. We also find that age structure differences can account for just over half of the variation in worldwide per capita GDP (i.e. the lack of sigma convergence) observed since 1960.