On Infinitely Divisible Exponential Dispersion Model Related to Poisson-Exponential Distribution

We construct a univariate exponential dispersion model comprised of discrete infinitely divisible distributions. This model emerges in the theory of branching processes. We obtain a representation for the Lévy measure of relevant distributions and characterize their laws as Poisson mixtures and/or compound Poisson distributions. The regularity of the unit variance function of this model is employed for the derivation of approximations by the Poisson-exponential model. We emphasize the role of the latter class. We construct local approximations relating them to properties of special functions and branching diffusions.     

Goodness-of-Fit Tests for the Skew-Normal Distribution When the Parameters Are Estimated from the Data

In this article, tests are developed which can be used to investigate the goodness-of-fit of the skew-normal distribution in the context most relevant to the data analyst, namely that in which the parameter values are unknown and are estimated from the data. We consider five test statistics chosen from the broad Cramér–von Mises and Kolmogorov–Smirnov families, based on measures of disparity between the distribution function of a fitted skew-normal population and the empirical distribution function. The sampling distributions of the proposed test statistics are approximated using Monte Carlo techniques and summarized in easy to use tabular form. We also present results obtained from simulation studies designed to explore the true size of the tests and their power against various asymmetric alternative distributions.     

Weighted Multivariate Tests of Independence

We present new tests of marginal independence for ?^d-valued random vectors. Our tests rely upon weighted Cramér–von Mises-type statistics, which are functionals of the empirical copula process based upon a random sample of size n. We establish a decomposition of this process into asymptotically independent components, and describe the tests which follow from these arguments.     

Confidence Bounds and Hypothesis Tests for Normal Distribution Coefficients of Variation

For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.     

Semiparametric Efficient Distribution Free Estimation of Panel Models

This article generalizes results from Park et al. (1998 Park , B. U. , Sickles , R. C. , Simar , L. ( 1998 ). Stochastic frontiers: a semiparametric approach . J. Econometrics 84 : 273 – 301 .[Crossref], [Web of Science ®] , [Google Scholar]) and Adams et al. (1999 Adams , R. M. , Berger , A. N. , Sickles , R. C. ( 1999 ). Semiparametric approaches to stochastic panel frontiers with applications in the banking industry . J. Bus. Econ. Statist. 17 : 349 – 358 .[Taylor & Francis Online] , [Google Scholar]) on semiparametric efficient estimation of panel models. The form of semiparametric efficient estimators depends on the statistical assumptions imposed. Normality assumptions on the transitory error are sometimes inappropriate. We relax the normality assumption used in the articles above to derive more general semiparametric efficient estimators. These estimators are illustrated in a Monte Carlo simulation and an analysis of banking productivity.     

Copulas with Truncation-Invariance Property

For a truncation-invariant copula, truncation does not change the dependence structure as well as all nonparametric measures of association such as Kendall's tau and Spearman's rho. In this article, we show that the products of algebraically independent Archimedean multivariate Clayton copulas and standard uniform distributions are the only truncation-invariant copulas.     

A Discrete Distribution Arising as a Solution of a Linear Difference Equation: Extension of the Non Central Negative Binomial Distribution

This article considers a discrete distribution that arises as the dominant solution of a linear difference equation. Basic properties and various chance mechanisms that lead to this distribution are given. In particular, its formulation as a weighted distribution and a mixed Poisson process are proposed. Parameter estimation by (a) using a combination of observed frequencies and moments and (b) maximum likelihood are examined. An example of goodness of fit is considered.     

Testing for Covariate Effect in the Cox Proportional Hazards Regression Model

This article presents methods for testing covariate effect in the Cox proportional hazards model based on Kullback–Leibler divergence and Renyi's information measure. Renyi's measure is referred to as the information divergence of order γ (γ ≠ 1) between two distributions. In the limiting case γ → 1, Renyi's measure becomes Kullback–Leibler divergence. In our case, the distributions correspond to the baseline and one possibly due to a covariate effect. Our proposed statistics are simple transformations of the parameter vector in the Cox proportional hazards model, and are compared with the Wald, likelihood ratio and score tests that are widely used in practice. Finally, the methods are illustrated using two real-life data sets.