We introduce new applications of the skew-probit IRT model by considering a flexible skew-normal distribution for the latent variables and by extending this model to include an additional random effect for modeling dependence between items within the same testlet. A Bayesian hierarchical structure is presented using a double data augmentation approach. This can be easily implemented in WinBUGS or SAS by considering MCMC algorithms. Several Bayesian model selection criteria, such as DIC, EAIC and EBIC, have been considered; in addition, we use posterior sum of squares of the latent residuals as a global discrepancy measure to model comparison. Two applications illustrate the methodology, one data set related to a mathematical test and another related to reading comprehension, both applied to Peruvian students. Results indicate better performance of the more flexible models proposed in this paper.

In this article, we employ the jackknife method of estimation and the concept of Studentized $U$-statistics to derive a new weak convergence result for nondegenerate $U$-statistics on the space $D[0,1]$. We drop the classical condition that the second moment of the kernel of the underlying $U$-statistic exists and derive a weighted weak convergence result for these Studentized statistics. This weak convergence is concluded from a weighted approximation in sup-norm $\|/q\|$, in probability, of Studentized $U$-statistics by partial sums of i.i.d. projections, where $q$ is in an appropriate class of positive weight functions.

This paper provides a means, using latent variables, to undertake a Bayesian analysis for the Bingham distribution. To date, this has been problematic due to a nonclosed form for the normalizing constant. Previous approaches have relied on approximating the constant; something which is unnecessary in the method adopted here.

Let ${\mathcal{Z}}$ be a so-called well-behaved percolation, that is, a certain random closed set in the hyperbolic plane, whose law is invariant under all isometries; for example, the covered region in a Poisson Boolean model. In terms of the $\alpha$-value of ${\mathcal{Z}}$, the Hausdorff-dimension of the set of directions is determined in which visibility from a fixed point to the ideal boundary of the hyperbolic plane is possible within ${\mathcal{Z}}$. Moreover, the Hausdorff-dimension of the set of (hyperbolic) lines through a fixed point contained in ${\mathcal{Z}}$ is calculated. Thereby several conjectures raised by Benjamini, Jonasson, Schramm and Tykesson are confirmed.

Linear regressions fitted to cross-sectional data oftentimes display heteroskedasticity, that is, error variances that are not constant. A common modeling strategy consists of estimating the regression parameters by ordinary least squares and then performing hypothesis testing inference using standard errors that are robust to heteroskedasticity. These tests have the correct size asymptotically regardless of whether the error variances are constant. In finite samples, however, they can be quite size-distorted. In this paper, we propose new heteroskedasticity-consistent covariance matrix estimators that deliver more reliable testing inferences in samples of small sizes.

In this work, we deal with a backward stochastic differential equation with respect to a Brownian motion and a Poisson random measure. We first establish existence and uniqueness of solution in the case of non-Lipschitz drift. In the second part, we prove a Large Deviation Principle for a family of solutions.

With the objective of analysing categorical data with missing responses, we extend the multinomial modelling scenario described by Paulino (Braz. J. Probab. Stat. 5 (1991) 1–42) to a product-multinomial framework that allows the inclusion of explanatory variables. We consider maximum likelihood (ML) and weighted least squares (WLS) as well as a hybrid ML/WLS approach to fit linear, log-linear and more general functional linear models under ignorable and nonignorable missing data mechanisms. We express the results in an unified matrix notation that may be easily used for their computational implementation and develop such a set of subroutines in R. We illustrate the procedures with the analysis of two data sets, and perform simulations to assess the properties of the estimators.

If $\alpha_{1}-\beta_{1}$ is an integer, then ${}_{p}F_{q}(\boldsymbol{\alpha} ;\boldsymbol{\beta} :z)$ can be expressed in terms of ${}_{p-1}F_{q-1}$. This leads to a conjectured generalization of Kummer’s transformation from ${}_{1}F_{1}$ to ${}_{p}F_{q}$. Applications are given for noncentral chi-square and Student’s $t$ distributions.