Estimating a uniform distribution when data are measured with a normal additive error with unknown variance

The problem of estimating the width of a symmetric uniform distribution on the line together with the error variance, when data are measured with normal additive error, is considered. The main purpose is to analyse the maximum-likelihood (ML) estimator and to compare it with the moment-method estimator. It is shown that this two-parameter model is regular so that the ML estimator is asymptotically efficient. Necessary and sufficient conditions are given for the existence of the ML estimator. As numerical problems are known to frequently occur while computing the ML estimator in this model, useful suggestions for computing the ML estimator are also given.     

Divergence-based tests of homogeneity for spatial data

The problem of testing homogeneity in contingency tables when the data are spatially correlated is considered. We derive statistics defined as divergences between unrestricted and restricted estimated joint cell probabilities and we show that they are asymptotically distributed as linear combinations of chi-square random variables under the null hypothesis of homogeneity. Monte Carlo simulation experiments are carried out to investigate the behavior of the new divergence test statistics and to make comparisons with the statistics that do not take into account the spatial correlation. We show that some of the introduced divergence test statistics have a significantly better behavior than the classical chi-square test for the problem under consideration when we compare them on the basis of the simulated sizes and powers.     

A note on a family of criteria for evaluating test statistics

ABSTRACT

In noting that the usual criteria for choosing an optimal test, Uniform Power and Local Power are at opposite ends of a spectrum of dominance criteria, a complete “Power Dominance” family of criteria for classifying and choosing optimal tests on the basis of their power characteristics is identified, wherein successive orders of dominance attach increasing weight to power close to the null hypothesis. Indices of the extent to which a preferred test has superior power characteristics over other members in its class, and an index of the proximity of a test to the envelope function of alternative tests are also provided. The ideas are exemplified using various optimal test statistics for Normal and Laplace population distributions.     

Time series in m-dimensions definition,problems and prospects

We define time series in m dimensions x, as follows: the observed variable z depends on and similarly n time series in m variables where f(x,t) and x are vectors. This is the discrete case. The continuous case is similar. Distinction is made between m time series in zero dimension, at a particular point x, and one time series in m dimensions.     

The quotient of two correlated normal variables with applications

The purpose of this paper is to present new results on the distribution of the quotient of two correlated normal variables and its use to solve many outstanding problems in all fields of science, economics, industry, commerce, education, and medicine. The results are relatively simple and may encourage one to use the exact distribution of the quotient. Examples in medicine, economics and industry will illustrate the applications. Further, these results open a new vista for the solution not only of problems involving bivariate distributions but also multivariate distributions.     

Perceptions of Migration and Diversity by Local Public Administrators

This article contributes to the recent debate on the perception of migration and diversity; it empirically examines whether public decision-makers and public administrators perceive migration and diversity as related or if they distinguish between them. It also seeks to identify the most important characteristics of respondents with positive attitudes to migration and diversity. The sample of the respondents covers Turkey, Greece, Hungary and Slovakia; those located on the “Balkan migration route” into Europe. Due to different experiences, respondents from countries with large-scale migration perceive migration and diversity differently from those in countries directly threatened by migration or countries without any direct impact of migration. Gender appears to be a statistically significant predictor in the need for high managerial skills to manage migration and diversity. Some size categories of municipalities where a respondent works appear to be statistically significant when ranking the local impacts and local economic benefits of migration.     

Flora of the tram tracks of Bratislava

Urban Ecosystems - Tram and railway tracks represent specific urban habitats, which host a specific type of flora. This study aims to compile the information about species composition of flora of...     

An optimal search procedure

Consider the following problem. There are exactly two defective (unknown) elements in the set X={x₁, x₂,…,x_n}, all possibilities occuring with equal probabilities. We want to identify the unknown (defective) elements by testing some subsets A of X, and for each such set A determining whether A contains any of them. The test on an individual subset A informs us that either all elements of the tested set A are good, or that at least one of them is defective (but we do not know which ones or how many). A set containing at least one defective element is said to be defective. Our aim is to minimize the maximal number of tests. For the optimal strategy, let the maximal test length be denoted by l₂(n). We obtain the value of this function for an infinite sequence of values of n.