A test for the equality of k medians against the simple tree alternative under right censorship

We consider a test for the equality of k population medians, θ_i i=1,2,….,k, when it is believed a priori, that θ _i: The observations are subject to right censorhip. The distributions of the censoring variables for each population are assumed to be equal. This test is compared with the general k-sample test proposed by Breslow     

Gibbs sampling for marginal posterior expectations

In earlier work (Gelfand and Smith, 1990 and Gelfand et al, 1990) a sampling based approach using the Gibbs sampler was offered as a means for developing marginal posterior densities for a wide range of Bayesian problems several of which were previously inaccessible. Our purpose here is two-fold. First we flesh out the implementation of this approach for calculation of arbitrary expectations of interest. Secondly we offer comparison with perhaps the most prominent approach for calculating posterior expectations, analytic approximation involving application of the LaPlace method. Several illustrative examples are discussed as well. Clear advantages for the sampling based approach emerge.     

Inferences on regression coefficients in a regression model under heteroscedasticity and robustness with respect to departure from normality

In this paper we consider a simple linear regression model under heteroscedasticity and nonnormality. A statistical test for testing the regression coefficient is then derived by assuming normality for the random disturbances and by applying Welch's method. Some Monte Carlo studies are generated for assessing robustness of this test. By combining Tiku's robust procedure with the new test, a robust but more powerful test is developed.     

Outlier detection by robust principal components analysis

The robust principal components analysis (RPCA) introduced by Campbell (Applied Statistics 1980, 29, 231–237) provides in addition to robust versions of the usual output of a principal components analysis, weights for the contribution of each point to the robust estimation of each component. Low weights may thus be used to indicate outliers. The present simulation study provides critical values for testing the kth smallest weight in the RPCA of a sample of n p-dimensional vectors, under the null hypothesis of a multivariate normal distribution. The cases p=2(2)10, 15, 20 for n=20, 30, 40, 50, 75, 100 subject to n≥p/2, are examined, with k≤√n.     

A simple approximation for the doubly noncentral t-distribution

A simple approximation for the doubly noncentral t-distribution, based upon the Fieller-Geary Theorem (1930) and approximate normality of the square root of the noncentral chi-square variable observed by Patnaik (1949), is developed, This approximation and an Edgeworth series expansion associated with it are evaluated. The simple approximation is seen to be reasonably accurate for most practical purposes.     

Bayesian inference of asymmetric stochastic conditional duration models

This paper extends stochastic conditional duration (SCD) models for financial transaction data to allow for correlation between error processes and innovations of observed duration process and latent log duration process. Suitable algorithms of Markov Chain Monte Carlo (MCMC) are developed to fit the resulting SCD models under various distributional assumptions about the innovation of the measurement equation. Unlike the estimation methods commonly used to estimate the SCD models in the literature, we work with the original specification of the model, without subjecting the observation equation to a logarithmic transformation. Results of simulation studies suggest that our proposed models and corresponding estimation methodology perform quite well. We also apply an auxiliary particle filter technique to construct one-step-ahead in-sample and out-of-sample duration forecasts of the fitted models. Applications to the IBM transaction data allow comparison of our models and methods to those existing in the literature.     

Approximate Bayesian Computation for Exponential Random Graph Models for Large Social Networks

We consider the issue of sampling from the posterior distribution of exponential random graph (ERG) models and other statistical models with intractable normalizing constants. Existing methods based on exact sampling are either infeasible or require very long computing time. We study a class of approximate Markov chain Monte Carlo (MCMC) sampling schemes that deal with this issue. We also develop a new Metropolis–Hastings kernel to sample sparse large networks from ERG models. We illustrate the proposed methods on several examples.     

Some small-sample results on a bounded influence rank regression method

Naranjo and HeUmansperger (1994) recently derved a bounded influence rank regression method and suggested how hypotheses about the regression coefficients might be tested. This brief note reports some simulation results on how their procedure performs when there is one predictor. Even when the error term is highly skewed, good control over the Type I error probability is obtained Power can be high relative to least squares regression when the error term has a heavy tailed distribution .and the predictor has a symmetric distribution However, if the predictor has a skewed distribution, power can be relatively low even when the distribution of the error term is heavy tailed. Despite this, it is argued that their method provides an important and useful alternative to ordinary least squares as well as other robust regression methods.     

Testing non-oblique hypotheses

This paper considers a likelihood ratio test for testing hypotheses defined by non-oblique closed convex cones, satisfying the so called iteration projection property, in a set of k normal means. We obtain the critical values of the test using the Chi-Bar-Squared distribution. The obtuse cones are introduced as a particular class of cones which are non-oblique with every one of their faces. Examples with the simple tree order cone and the total order cone are given to illustrate the results.     

Distribution theory and inference for polynomial-normal densities

This paper considers a class of densities formed by taking the product of nonnegative polynomials and normal densities. These densities provide a rich class of distributions that can be used in modelling when faced with non-normal characteristics such as skewness and multimodality. In this paper we address inferential and computational issues arising in the practical implementation of this parametric family in the context of the linear model. Exact results are recorded for the conditional analysis of location-scale models and an importance sampling algorithm is developed for the implementation of a conditional analysis for the general linear model when using polynomial-normal distributions for the error.