A New Spatial Skew-Normal Random Field Model

Skewness is often present in a wide range of geostatistical problems, and modeling it in the spatial context remains a challenging problem. In this article, we propose and study a new class of spatial skew-normal random fields, defined in terms of the closed multivariate skew-normal distribution. Such fields can be written as the sum of two independent fields: one Gaussian and the other truncated Gaussian. We derive theoretical expressions for the first- and second-order moments, and use them within a method of moments based procedure to estimate the parameters of the model. Data simulated from the model are used to illustrate the methodology developed.     

One-sample location tests for multilevel data

In this paper, we consider testing the location parameter with multilevel (or hierarchical) data. A general family of weighted test statistics is introduced. This family includes extensions to the case of multilevel data of familiar procedures like the t, the sign and the Wilcoxon signed-rank tests. Under mild assumptions, the test statistics have a null limiting normal distribution which facilitates their use. An investigation of the relative merits of selected members of the family of tests is achieved theoretically by deriving their asymptotic relative efficiency (ARE) and empirically via a simulation study. It is shown that the performance of a test depends on the clusters configurations and on the intracluster correlations. Explicit formulas for optimal weights and a discussion of the impact of omitting a level are provided for 2 and 3-level data. It is shown that using appropriate weights can greatly improve the performance of the tests. Finally, the use of the new tests is illustrated with a real data example.     

Dickey-fuller tests with trend

The Dickey-Fuller [rcirc]_τ and [pcirc]_τ tests are based on a regression of a variable on its lagged value, an intercept, and a trend term. The distributions of both statistics depend on the coefficient of the trend, and the usual Dickey-Fuller tabulations assume that this coefficient equals zero. This paper provides tabulations for the case that the coefficient of the trend is non-zero.     

A weighted spatial median for clustered data

A weighted spatial median is proposed for the multivariate one-sample location problem with clustered data. Its limiting distribution is derived under mild conditions (no moment assumptions) and it is shown to be multivariate normal. Asymptotic as well as finite sample efficiencies and breakdown properties are considered, and the theoretical results are supplied with illustrative examples. It turns out that there is a potential for meaningful gains in estimation efficiency: the weighted spatial median has superior efficiency to the unweighted spatial median particularly when the cluster sizes are widely disparate and in the presence of strong intracluster correlation. The unweighted spatial median for clustered data was considered earlier by Nevalainen et al. (Can J Statist, in press, 2007). The proposed weighted estimators provide companion estimates to the weighted affine invariant sign test proposed recently by Larocque et al. (Biometrika, in press, 2007). An affine equivariant weighted spatial median is discussed in parallel.     

FAMILY STRUCTURES OF ASSAULTIVE ADOLESCENTS

This study compared 17 assaultive adolescents and 12 nonassaultive adolescents on a measure of family structure which assesses the family's perceptions of the authority hierarchy and the amount of closeness and distance between family members. The results demonstrated that the experimental group significantly more often perceived the presence of a reversal in the generational hierarchy of authority. The authors discuss the meaning of these results as they relate to violent teenagers and their family interactions.