A Matrix Variate Closed Skew-Normal Distribution with Applications to Stochastic Frontier Analysis

In this article, we introduce the matrix extension of the closed skew-normal distribution and give two constructions for it: a marginal one and another based on hidden truncation. Important basic properties of the distribution are presented such as its closure under linear transformation and moment generating function. We also give distributional results for quadratic forms involving random matrices distributed according to two particular cases of it. Using an additive construction, we derive a submodel which can be employed to describe the compound error structure of a very general multivariate stochastic frontier model. Finally, we consider the skew-elliptical extension of the proposed distribution.     

Nonparametric comparison of curves with dependent errors

Suppose that data {(x _l,i,n , y _l,i,n ): l?=?1, …, k; i?=?1, …, n} are observed from the regression models: Y _l,i,n ?=?m _l (x _l,i,n )?+?? _l,i,n , l?=?1, …, k, where the regression functions {m _l } _l=1 ^k are unknown and the random errors {? _l,i,n } are dependent, following an MA(∞) structure. A new test is proposed for testing the hypothesis H ₀: m ₁?=?·?·?·?=?m _k , without assuming that {m _l } _l=1 ^k are in a parametric family. The criterion of the test derives from a Crámer-von-Mises-type functional based on different distances between {[mcirc]} _l and {[mcirc]} _s , l?≠?s, l, s?=?1, …, k, where {[mcirc] _l } _l=1 ^k are nonparametric Gasser–Müller estimators of {m _l } _l=1 ^k . A generalization of the test to the case of unequal design points, with different sample sizes {n _l } _l=1 ^k and different design densities {f _l } _l=1 ^k , is also considered. The asymptotic normality of the test statistic is obtained under general conditions. Finally, a simulation study and an analysis with real data show a good behavior of the proposed test.     

Random translation of discrete order statistics

We investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose order statistics are related by a random translation. We also provide some examples using the constructive method that we propose.     

Importance of the prior mass for agreement between frequentist and Bayesian approaches in the two-sided test

We study distributional properties of generalized order statistics (gos) related by a random shift or scaling scheme in the continuous and discrete case, respectively. In the continuous case, we obtain new characterizations of distributions relating non-neighbouring gos extending some results given in the literature for the neighbouring cases. On the other hand, in the discrete case, we investigate the existence and uniqueness of a discrete parent distribution supported on the integers whose gos are related by a random translation.     

Testing for spherical symmetry via the empirical characteristic function

Kolmogorov–Smirnov-type and Cramér–von Mises-type goodness-of-fit tests are proposed for the null hypothesis that the distribution of a random vector X is spherically symmetric. The test statistics utilize the fact that X has a spherical symmetric distribution if, and only if, the characteristic function of X is constant over surfaces of spheres centred at the origin. Both tests come in convenient forms that are straightforwardly applicable with the computer. The asymptotic null distribution of the test statistics as well as the consistency of the tests is investigated under general conditions. Since both the finite sample and the asymptotic null distribution depend on the unknown distribution of the Euclidean norm of X, a conditional Monte Carlo procedure is used to actually carry out the tests. Results on the behaviour of the test in finite-samples are included along with a real-data example.     

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.     

Lower posterior death probabilities from a quick medical response in road traffic accidents

Introduction: We use data from Spain on roads and motorways traffic accidents in May 2004 to quantify the statistical association between quick medical response time and mortality rate. Method: Probit and logit parameters are estimated by a Bayesian method in which samples from the posterior densities are obtained through an MCMC simulation scheme. We provide posterior credible intervals and posterior partial effects of a quick medical response at several time levels over which we express our prior beliefs. Results: A reduction of 5 min, from a 25-min response-time level, is associated with lower posterior probabilities of death in roads and motorways accidents of 24% and 30%, respectively.     

Bayesian influence diagnostics in radiocarbon dating

Linear models constitute the primary statistical technique for any experimental science. A major topic in this area is the detection of influential subsets of data, that is, of observations that are influential in terms of their effect on the estimation of parameters in linear regression or of the total population parameters. Numerous studies exist on radiocarbon dating which propose a value consensus and remove possible outliers after the corresponding testing. An influence analysis for the value consensus from a Bayesian perspective is developed in this article.     

An Exponential Model for Damage Accumulation

In this article, we present a general model for predicting the fatigue behavior for any stress level and amplitude using the exponential model. Based on the Wöhler field for fixed stress level, a compatibility functional equation enables us to derive the general model with eight parameters. The problem of parameter estimation is then discussed and some methods are described. Some examples are finally presented to illustrate the derived model and the proposed methods of estimation.     

Developing an Index to Measure Sub-municipal Level Urban Sprawl

The present study aims to develop an index composed of different spatial variables to measure the urban sprawl levels of a municipality located in Southern Spain. According to the findings, urban sprawl can be measured not only on the metropolitan level but also on a more detailed and precise level, such as sub-municipal. A group of experts chosen for their suitability in measuring urban sprawl select six spatial variables (population density, net residential density, coverage ratio, land use types, percentage of residential land use, and average year of construction). These variables are aggregated using Choquet integral, a technique that combines interactions between those variables providing greater coherence to the complexity that is inherent in the creation of composite sprawl indexes. This methodology has been demonstrated to be valid and appropriate in evaluating urban expansion at sub-municipal level, but can also be applied to other scales once it is clearly a phenomenon in which interaction between criteria exists. The resulting composite index allows the assignment of different levels of sprawl to the urban areas consistent with their morphology and landscape.