On the matrix-variate generalized hyperbolic distribution and its Bayesian applications

In the first part of the paper, we introduce the matrix-variate generalized hyperbolic distribution by mixing the matrix normal distribution with the matrix generalized inverse Gaussian density. The p-dimensional generalized hyperbolic distribution of [Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat., 5, 151–157], the matrix-T distribution and many well-known distributions are shown to be special cases of the new distribution. Some properties of the distribution are also studied. The second part of the paper deals with the application of the distribution in the Bayesian analysis of the normal multivariate linear model.     

On construction of exact experimental designs from discrete ones

In the paper we try to evaluate approximately optimum exact designs of required goodness from a known approximately optimum discrete design. In dependence on this discrete design we define some subsets of the set of all considered exact designs.

Then we look for sufficiency conditions, on which elements of these subsets are approximately optimum (exact) designs of the required goodness. Moreover we offer a method to find such elements, if they exist at all. Finally we prove some statements concerning the existence of such elements for two classes of (optimum) criteria.     

Two-sample Pitman closeness comparison under progressive Type-II censoring

In this paper, we consider two problems concerning two independent progressively Type-II censored samples. We first consider the Pitman closeness (PC) of order statistics from two independent progressively censored samples to a specific population quantile. We then consider the point prediction of a future progressively censored order statistic and discuss the determination of the closest progressively censored order statistic from the current sample according to the simultaneous closeness probabilities. For both these problems, explicit expressions are derived for the pertinent PC probabilities, and then special cases are given as examples. For various censoring schemes, we also present numerical results for the standard uniform, standard exponential, and standard normal distributions. Finally, a distribution-free result for the median is obtained.     

Estimating prediction error in microarray classification: Modifications of the 0.632+ bootstrap when ${\bf n} < {\bf p}$

We are interested in estimating prediction error for a classification model built on high dimensional genomic data when the number of genes (p) greatly exceeds the number of subjects (n). We examine a distance argument supporting the conventional 0.632+ bootstrap proposed for the $n > p$ scenario, modify it for the $n < p$ situation and develop learning curves to describe how the true prediction error varies with the number of subjects in the training set. The curves are then applied to define adjusted resampling estimates for the prediction error in order to achieve a balance in terms of bias and variability. The adjusted resampling methods are proposed as counterparts of the 0.632+ bootstrap when $n < p$ , and are found to improve on the 0.632+ bootstrap and other existing methods in the microarray study scenario when the sample size is small and there is some level of differential expression. The Canadian Journal of Statistics 41: 133–150; 2013 © 2012 Statistical Society of Canada     

Hierarchical modeling with gaussian processes

We formulate a hierarchical version of the Gaussian Process model. In particular, we assume there to be data on several units randomly drawn from the same population. For each unit, several responses are available that arise from a Gaussian Process model. The parameters characterizing the Gaussian Process model for the units are modeled to arise from normal or gamma distributions. Results for two simulations are given that compare the performance of the hierarchical and non-hierarchical models.     

Comparison of prediction methods for multicollinear data

In this paper we discuss the partial least squares (PLS) prediction method. The method is compared to the predictor based on principal component regression (PCR). Both theoretical considerations and computations on artificial and real data are presented.     

On Mean Squared Prediction Error Estimation in Small Area Estimation Problems

For a general linear mixed normal model, a new linearized weighted jackknife method is proposed to estimate the mean squared prediction error (MSPE) of an empirical best linear unbiased predictor (EBLUP) of a general mixed effect. Different MSPE estimators are compared using a Monte Carlo simulation study.     

A Monte Carlo Method for Estimating Prediction Limit for the Arithmetic Mean of Lognormal Sample

A Monte Carlo (MC) method is suggested for calculating an upper prediction limit for the mean of a future sample of small size N from a lognormal distribution. This is done by obtaining a Monte Carlo estimator of the limit utilizing the future sample generated from the Gibbs sampler. For the Gibbs sampler, a full conditional posterior predictive distribution of each observation in the future sample is derived. The MC method is straightforward to specify distributionally and to implement computationally, with output readily adapted for required inference summaries. In an example, practical application of the method is described.     

Linear Prediction Sufficiency for New Observations in the General Gauss–Markov Model

We consider the prediction of new observations in a general Gauss–Markov model. We state the fundamental equations of the best linear unbiased prediction, BLUP, and consider some properties of the BLUP. Particularly, we focus on such linear statistics, which preserve enough information for obtaining the BLUP of new observations as a linear function of them. We call such statistics linearly prediction sufficient for new observations, and introduce some equivalent characterizations for this new concept.