Goodness-of-fit tests for Pareto distribution based on a characterization and their asymptotics

In this paper we present a new characterization of the Pareto distribution and consider goodness-of-fit tests based on it. We provide an integral and Kolmogorov–Smirnov-type statistics based on U-statistics and we calculate Bahadur efficiency for various alternatives. We find locally optimal alternatives for those tests. For small sample sizes, we compare the power of those tests with some common goodness-of-fit tests.     

A bibliography of statistical tolerance regions

The bibliography contains about 270 references dealing with statistical tolerance regions. These are classified according to the type of probability distribution concerned and according to some other criteria as well.     

A bibliography of statistical tolerance regions,II

This bibiliography (completing the previous one, JILEK 1981a) contains about 130 references dealing with statistical tolerance regions. References are classified according to the type of probability distribution concerned and according to some other criteria as well     

Comparison of efficiencies of some symmetry tests around an unknown centre

In this paper, some recent and classical tests of symmetry are modified for the case of an unknown centre. The unknown centre is estimated with its α-trimmed mean estimator. The asymptotic behaviour of the new tests is explored. The local approximate Bahadur efficiency is used to compare the tests to each other as well as to some other tests.     

Two-dimensional Kolmogorov-type goodness-of-fit tests based on characterisations and their asymptotic efficiencies

In this paper, new two-dimensional goodness-of-fit tests are proposed. They are of supremum type and are based on two different types of characterisations. The first type are those that involve functional equations that the distribution function satisfies, while the second type uses independence of some statistics. The asymptotics of the statistics is studied and Bahadur efficiencies of the tests against some close alternatives are calculated. In the process, a theorem on large deviations of Kolmogorov-type statistics has been extended to the multidimensional case.     

DO IMMIGRANTS CAUSE CRIME?

We examine the empirical relationship between immigration and crime across Italian provinces during the period 1990–2003. Drawing on police administrative records, we first document that the size of the immigrant population is positively correlated with the incidence of property crimes and with the overall crime rate. Then, we use instrumental variables based on immigration toward destination countries other than Italy to identify the causal impact of exogenous changes in Italy’s immigrant population. According to these estimates, immigration increases only the incidence of robberies, while leaving unaffected all other types of crime. Since robberies represent a very minor fraction of all criminal offenses, the effect on the overall crime rate is not significantly different from zero.