A characterization of the bivariate elliptically contoured distribution

The Cauchy distribution of the quotient of two random variables and its independence of the sum of squares of them together with some symmetry assumptions are the characteristic property of the bivariate elliptically contoured measures.     

Assessment of the Living Conditions in Polish and German Transborder Regions in the Context of Strengthening Territorial Cohesion in the European Union: Competitiveness or Complementation?

Social Indicators Research - The European Union's regional policy aims to strengthen economic, social, and territorial cohesion and equal space development opportunities. It is an action...     

A binary control chart to detect small jumps

The classic N p-chart gives a signal if the number of successes in a sequence of independent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is superior in terms of out-of-control average run length, when one is interested in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives, which explains that unexpected and interesting behaviour. Since real observations are often not independent, the question arises whether these results still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, first, to a large class of time series models, and, second, to locally dependent image data, as we demonstrate by an example.     

Flattening topologically spherical surface

The problem of optimal surface flattening in 3-D finds many applications in engineering and manufacturing. However, previous algorithms for this problem are all heuristics without any quality guarantee and the computational complexity of the problem was not well understood. In this paper, we prove that the optimal surface flattening problem is NP-hard. Further, we show that the problem of flattening a topologically spherical surface admits a PTAS and can be solved by a (1+ε)-approximation algorithm in O(nlog n) time for any constant ε>0, where n is the input size of the problem.     

Spillover effects of taxes on government debt: a spatial panel approach

It is claimed that tax policy is neither time- nor space-independent due to cross-border tax base mobility, which induces spillovers. Specifically, fiscal shocks in one country are supposed to have an impact on fiscal policies in other countries. Different types of taxes influence economies differently. This paper addresses the question of their impact on government debt. Within a framework of spatial econometric modeling, we evaluate the impact of capital, labor and consumption taxes on public debt in 34 European countries in 2002–2011, and find strong spatial spillovers. We show that a consumption tax and, to a lesser degree, a capital tax significantly affect the sovereign debt, and that the global relations play a leading role (i.e. dominate the local ones) in shaping fiscal policy.     

Estimation of the quantile function using Bernstein–Durrmeyer polynomials

This paper studies quantile estimation using Bernstein–Durrmeyer polynomials in terms of its mean squared error and integrated mean squared error including rates of convergence as well as its asymptotic distribution. Whereas the rates of convergence are achieved for i.i.d. samples, we also show that the consistency more or less directly follows from the consistency of the sample quantiles, such that our proposal can also be applied for risk measurement in finance and insurance. Furthermore, an improved estimator based on an error-correction approach is proposed for which a general consistency result is established. A crucial issue is how to select the degree of Bernstein–Durrmeyer polynomials. We propose a novel data-adaptive approach that controls the number of modes of the corresponding density estimator. Its consistency including an uniform error bound as well as its limiting distribution in the sense of a general invariance principle are established. The finite sample properties are investigated by a Monte Carlo study. Finally, the results are illustrated by an application to photovoltaic energy research.     

On Existence of Maximum Likelihood Estimators in Exponential Families

We propose a simple necessary and sufficient condition for existence of maximum likelihood estimators in a large class of canonical exponential families. We give an application to log-spline families.     

Linearity of regression for the past weak and ordinary records

In this paper we study the property of linearity of backward regression for non-adjacent records. In the case of weak records, a characterization of the geometric distribution is obtained. It also appears that a related characterization for ordinary records does not hold, showing the difference in conditional behaviour between weak and ordinary records.     

Allocation Constraints in Stratification

When a finite population is to be stratified, one of constraints in stratification is that sample sizes from strata may not be greater than the corresponding stratum sizes and may not be smaller than two. There are several ways of treating this allocation constraint, each providing an alternative approach to stratification. In this article, it is shown that a choice of the approach has a bearing on stratification efficiency. Unfortunately, no particular approach out of the four compared is shown to be the most efficient for each population studied. In addition, the approaches are applied to stratify a real population.