Bayesian analysis of null intercept errors-in-variables regression for pretest/post-test data

This article discusses a Bayesian analysis of repeated measures pretest/post-test data under null intercepts errors-in-variables regression models. For illustration we consider an example in the field of dentistry involving the comparison of two types of toothbrushes with respect to the efficacy in removing dental plaque. The proposed Bayesian approach accommodates the correlated measurements and incorporates the restriction that the slopes must lie in the [0,1] interval, a feature not considered in the analysis conducted by Singer & Andrade (1997). The observed values of the (repeated) response and explanatory variables are supposed to follow a Multivariate Student- t distribution. A Gibbs sampler is used to perform the computations.     

Skew binary regression with measurement errors

In this paper, we extend the structural probit measurement error model by considering that the unobserved covariate follows a skew-normal distribution. The new model is termed the structural skew-normal probit model. As in the normal case, the likelihood function is obtained analytically which can be maximized by using existing statistical software. A Bayesian approach using Markov chain Monte Carlo techniques to generate from the posterior distributions is also developed. A simulation study demonstrates the usefulness of the approach in avoiding attenuation which is the case with the naive procedure and it seems to be more efficient than using the structural probit model when the distribution of the covariate (predictor) is skew.     

Generalized skew-normal models: properties and inference [Statistics 40 (2006) 495–505]

In [H.W. Gómez, H.S. Salinas and H. Bolfarine, Generalized skew-normal models: Properties and inference, Statistics 40(6) (2006), pp. 495–505] introduces a new family of asymmetric distributions that depends on two parameters called, α and β, such as for the particular case β = 0 obtained skew-normal distribution. In this note we give a corrected version for the expression that is used in calculating the moments of such distribution.     

An extension of the generalized half-normal distribution

In this paper we propose an extension of the generalized half-normal distribution studied in Cooray and Ananda (Commun Stat 37:1323–1337, 2008). This new distribution is defined by considering the quotient of two random variables, the one in the numerator being a generalized half normal distribution and the one in the denominator being a power of the uniform distribution on \((0,1)\) , respectively. The resulting distribution has greater kurtosis than the generalized half normal distribution. The density function of this more general distribution is derived jointly with some of its properties and moments. We discuss stochastic representation, maximum likelihood and moments estimation. Applications to real data sets are reported revealing that the proposed distribution can fit real data better than the slashed half-normal, generalized half-normal and Birnbaum–Saunders distributions.     

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.     

Influence Diagnostics for a Skew Extension of the Grubbs Measurement Error Model

Influence diagnostics methods are extended in this article to the Grubbs model when the unknown quantity x (latent variable) follows a skew-normal distribution. Diagnostic measures are derived from the case-deletion approach and the local influence approach under several perturbation schemes. The observed information matrix to the postulated model and Delta matrices to the corresponding perturbed models are derived. Results obtained for one real data set are reported, illustrating the usefulness of the proposed methodology.     

Bayesian analysis of generalized elliptical semi-parametric models

In this paper, we study the statistical inference based on the Bayesian approach for regression models with the assumption that independent additive errors follow normal, Student-t, slash, contaminated normal, Laplace or symmetric hyperbolic distribution, where both location and dispersion parameters of the response variable distribution include nonparametric additive components approximated by B-splines. This class of models provides a rich set of symmetric distributions for the model error. Some of these distributions have heavier or lighter tails than the normal as well as different levels of kurtosis. In order to draw samples of the posterior distribution of the interest parameters, we propose an efficient Markov Chain Monte Carlo (MCMC) algorithm, which combines Gibbs sampler and Metropolis–Hastings algorithms. The performance of the proposed MCMC algorithm is assessed through simulation experiments. We apply the proposed methodology to a real data set. The proposed methodology is implemented in the R package BayesGESM using the function gesm().     

On the Skew-Normal-Cauchy Distribution

A fixed effects one-way layout model of analysis of variance is considered where the variances are taken to be possibly unequal. Conservative single-stage procedures based on Banerjee’s method for the solution of the Behrens-Fisher problem are proposed for the following multiple comparisons problems: 1) all pairwise comparisons with a control population mean, and 2) all pairwise comparisons and all linear contrasts among the means. Since these procedures are likely to be very conservative in practice, approximate procedures based on Welch’s method for the solution of the Behrens-Fisher problem are suggested as alternatives. Monte Carlo studies indicate that the latter are much less conservative and hence may be better in practice. Both these sets of procedures need only the tables of the Student’s t-distribution for their application and are very simple to use. Exact two-stage procedures are proposed for the following multiple comparisons problems: 1) all pairwise comparisons and all linear contrasts among the means, and 2) all linear combinations of the means.     

Some asymptotic results in finite populations

In this paper we investigate limiting properties of predictors of some finite population quantities. Both, the sample size and the population size are considered to become large. Limiting properties like consistency and asymptotic normality of the best linear unbiased predictors of the population total and of the finite population regression coefficient are investigated.     

Constant hazard against a change-point alternative: a bayesian approach with censored data

A Bayesian approach to the problem of a constant hazard with a single change-point is developed using noninformative reference priors. We also present a generalization for the comparison for two treatments.