Modified D-optimal design for logistic model

Asymptotic theory of using the Fisher information matrix may provide poor approximation to the exact variance matrix of maximum likelihood estimation in nonlinear models. This may be due to not obtaining an efficient D-optimal design. In this article, we propose a modified D-optimality criterion, using a more accurate information matrix, based on the Bhattacharyya matrix. The proposed information matrix and its properties are given for two parameters simple logistic model. It is shown that the resulted modified locally D-optimal design is more efficient than the previous one; particularly, for small sample size experiments.     

A simple generalization of the Box–Muller method for obtaining a pair of correlated standard normal variables

In the simple and widely used method of Box–Muller [G. Box and M. Muller, A note on the generation of random normal deviates, Ann. Math. Statist. 29 (1958), pp. 610–611], from a pair of uniform and independent random variables in (0,1), a pair of standard and independent normal variables is obtained. In this article, we present a very simple and elegant generalization of this method to obtain a pair of correlated standard normal variables with a given coefficient of correlation. This generalized method, which is computationally very easy, is interpreted in geometric terms, considering a translation of the uniform interval (0,1) and a rotation of a defined angle, both related to the coefficient of correlation. Some numerical results are simulated and statistically analysed, proving that the generalization is extremely simple and powerful.     

Another extended Burr III model: some properties and applications

We introduce an extended Burr III distribution as an important model for problems in survival analysis and reliability. The new distribution can be expressed as a linear combination of Burr III distributions and then it has tractable properties for the ordinary and incomplete moments, generating and quantile functions, mean deviations and reliability. The density of its order statistics can be given in terms of an infinite linear combination of Burr III densities. The estimation of the model parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed model is applied to a real data set to illustrate its potentiality.     

On the Behrens–Fisher problem from the spatial median point of view

We present a non-parametric affine-invariant test for the multivariate Behrens–Fisher problem. The proposed method based on the spatial medians is asymptotic and does not require normality of the data. To improve its finite sample performance, we apply a correction of the type which was already used in a similar test based on trimmed means, however, our simulations show that in the case of heavy-tailed distributions our method performs better. Also in a simulation comparison with a recently published rank-based test our test yields satisfactory results.     

A test for the complete independence of high-dimensional random vectors

ABSTRACT

This paper discusses the problem of testing the complete independence of random variables when the dimension of observations can be much larger than the sample size. It is reported that two typical tests based on, respectively, the biggest off-diagonal entry and the largest eigenvalue of the sample correlation matrix lose their control of type I error in such high-dimensional scenarios, and exhibit distinct behaviours in type II error under different types of alternative hypothesis. Given these facts, we propose a permutation test procedure by synthesizing these two extreme statistics. Simulation results show that for finite dimension and sample size the proposed test outperforms the existing methods in various cases.     

Testing equality of correlation coefficients for paired binary data from multiple groups

Paired binary data arise naturally when paired body parts are investigated in clinical trials. One of the widely used models for dealing with this kind of data is the equal correlation coefficients model. Before using this model, it is necessary to test whether the correlation coefficients in each group are actually equal. In this paper, three test statistics (likelihood ratio test, Wald-type test, and Score test) are derived for this purpose. The simulation results show that the Score test statistic maintains type I error rate and has satisfactory power, and therefore is recommended among the three methods. The likelihood ratio test is over conservative in most cases, and the Wald-type statistic is not robust with respect to empirical type I error. Three real examples, including a multi-centre Phase II double-blind placebo randomized controlled trial, are given to illustrate the three proposed test statistics.     

Assessing inter- and intra-agreement for dependent binary data: a Bayesian hierarchical correlation approach

Agreement measures are designed to assess consistency between different instruments rating measurements of interest. When the individual responses are correlated with multilevel structure of nestings and clusters, traditional approaches are not readily available to estimate the inter- and intra-agreement for such complex multilevel settings. Our research stems from conformity evaluation between optometric devices with measurements on both eyes, equality tests of agreement in high myopic status between monozygous twins and dizygous twins, and assessment of reliability for different pathologists in dysplasia. In this paper, we focus on applying a Bayesian hierarchical correlation model incorporating adjustment for explanatory variables and nesting correlation structures to assess the inter- and intra-agreement through correlations of random effects for various sources. This Bayesian generalized linear mixed-effects model (GLMM) is further compared with the approximate intra-class correlation coefficients and kappa measures by the traditional Cohen’s kappa statistic and the generalized estimating equations (GEE) approach. The results of comparison studies reveal that the Bayesian GLMM provides a reliable and stable procedure in estimating inter- and intra-agreement simultaneously after adjusting for covariates and correlation structures, in marked contrast to Cohen’s kappa and the GEE approach.