An eigenproblem approach to optimal equal-precision sample allocation in subpopulations

Allocation of samples in stratified and/or multistage sampling is one of the central issues of sampling theory. In a survey of a population often the constraints for precision of estimators of subpopulations parameters have to be taken care of during the allocation of the sample. Such issues are often solved with mathematical programming procedures. In many situations it is desirable to allocate the sample, in a way which forces the precision of estimates at the subpopulations level to be both: optimal and identical, while the constraints of the total (expected) size of the sample (or samples, in two-stage sampling) are imposed. Here our main concern is related to two-stage sampling schemes. We show that such problem in a wide class of sampling plans has an elegant mathematical and computational solution. This is done due to a suitable definition of the optimization problem, which enables to solve it through a linear algebra setting involving eigenvalues and eigenvectors of matrices defined in terms of some population quantities. As a final result, we obtain a very simple and relatively universal method for calculating the subpopulation optimal and equal-precision allocation which is based on one of the most standard algorithms of linear algebra (available, e.g., in R software). Theoretical solutions are illustrated through a numerical example based on the Labour Force Survey. Finally, we would like to stress that the method we describe allows to accommodate quite automatically for different levels of precision priority for subpopulations.     

Barriers in Access to the Treatment for People with Gambling Disorders. Are They Different from Those Experienced by People with Alcohol and/or Drug Dependence?

A prevalence of gambling disorders is diversified depending on the region of the world. Almost three quarters of pathological gamblers had never sought a professional treatment as well as an assistance in self-help groups. Reasons why they do not initiate a treatment are complex. The aim of the article is to compare barriers to the treatment for people with gambling disorders found in presented study and barriers to alcohol and drug treatment identified in the available literature. The semi structured interviews were applied and conducted with people with gambling disorders, social workers, therapists employed in the addiction treatment facilities, General Practitioners and psychiatrists. Selection of the respondents was based on purposive sampling. In total, 90 interviews were completed. Respondents identified individual barriers as well as structural ones. Individual barriers include internal resistance and a fear of the treatment. In turn structural barriers apply to the organization of the therapy, infrastructure, personnel, and the therapeutic program. A comparison of barriers experienced by people with gambling disorders and substance use disorders showed that they are largely similar, but people with gambling disorders also experience specific barriers. Empirical studies focused specifically on treatment needs of people experiencing gambling disorders may improve an offer of help for them. More adequate treatment options could contribute to the increasing in the number of people who start the treatment. It can result in improving their quality of life and may have positive impact on public health.     

Performance of Preliminary Test Estimator Under Linex Loss Function

This article describes two bivariate geometric distributions. We investigate characterizations of bivariate geometric distributions using conditional failure rates and study properties of the bivariate geometric distributions. The bivariate models are fitted to real-life data using the Method of Moments, Maximum Likelihood, and Bayes Estimators. Two methods of moments estimators, in each bivariate geometric model, are compared and evaluated for their performance in terms of bias vector and covariance matrix. This comparison is done through a Monte Carlo simulation. Chi-square goodness-of-fit tests are used to evaluate model performance.     

Conditional specifications of multivariate pareto and student distributions

A random vector has a multivariate Pareto distribution if one of its univariate conditional distribution is Pareto and some of its marginals are identically distributed.A general method developed in the course of the proof of this result is applied also to characterize the multivariate Student (Cauchy) measure by one univariate Student conditional distribution.     

Shrinkage estimator of regression model under asymmetric loss

This article investigates the performance of the shrinkage estimator (SE) of the parameters of a simple linear regression model under the LINEX loss criterion. The risk function of the estimator under the asymmetric LINEX loss is derived and analyzed. The moment-generating functions and the first two moments of the estimators are also obtained. The risks of the SE have been compared numerically with that of pre-test and least-square estimators (LSEs) under the LINEX loss criterion. The numerical comparison reveals that under certain conditions the LSE is inadmissible, and the SE is the best among the three estimators.