Moments of the quartic assignment statistic with an application to multiple regression

We present the first three exact moments of the symmetric quartic assignment statistic. Efficient computational formulas have been derived to overcome severe difficulties in third moment calculations. Two examples illustrate applications of the quartic assignment statistic: evaluation of significant “clustering” or “mixing”; and distribution-free tests for equality of several planar regression models. This article extends previous results on the cubic assignment statistic in Iyer and Vecchia (1989).     

The likelihood ratio test foe the homogeneity of the variances in a covariance matrix with block compound symmetry

For the problem of testing the homogeneity of the variances in a covariance matrix with a block compound symmetric structure, the likelihood ratio test is derived in this paper, A modification of the test that allows its distribution to be better approximated by the chi-square distribution is also considered, Formulae for calculating approximate sample size and power are derived, Small sample performances of these tests in the case of two dependent bivariate or trivariate normals are compared to each other and to the competing tests by simulating levels of significance and powers, and recommendation is made of the ones that have good performance, The recommended tests are then demonstrated in an illustrative example.     

An approximation to the distribution of the ratio of two general quadratic forms with application

Based on mixed cumulants up to order six, this paper provides a four moment approximation to the distribution of a ratio of two general quadratic forms in normal variables. The approximation is applied to calculate the percentile points of modified F-test statistics for testing treatment effects when standard F-ratio test is misleading because of dependence among observations. For the special case, when data is generated by an AR(1) process, the approximation is evaluated by a simulation study. For the general SARMA (p,q)(P,Q)_s process, a modified F-test statistic Is given, and its distribution for the (0,1)(0,l)₁₂ process, is approximated by the moment approximation technique.     

An extensive power evaluation of a novel two-sample density-based empirical likelihood ratio test for paired data with an application to a treatment study of attention-deficit/hyperactivity disorder and severe mood dysregulation

In many case-control studies, it is common to utilize paired data when treatments are being evaluated. In this article, we propose and examine an efficient distribution-free test to compare two independent samples, where each is based on paired observations. We extend and modify the density-based empirical likelihood ratio test presented by Gurevich and Vexler [7] to formulate an appropriate parametric likelihood ratio test statistic corresponding to the hypothesis of our interest and then to approximate the test statistic nonparametrically. We conduct an extensive Monte Carlo study to evaluate the proposed test. The results of the performed simulation study demonstrate the robustness of the proposed test with respect to values of test parameters. Furthermore, an extensive power analysis via Monte Carlo simulations confirms that the proposed method outperforms the classical and general procedures in most cases related to a wide class of alternatives. An application to a real paired data study illustrates that the proposed test can be efficiently implemented in practice.     

EM algorithm-based likelihood estimation for a generalized Gompertz regression model in presence of survival data with long-term survivors: an application to uterine cervical cancer data

In this paper we develop a regression model for survival data in the presence of long-term survivors based on the generalized Gompertz distribution introduced by El-Gohary et al. [The generalized Gompertz distribution. Appl Math Model. 2013;37:13–24] in a defective version. This model includes as special case the Gompertz cure rate model proposed by Gieser et al. [Modelling cure rates using the Gompertz model with covariate information. Stat Med. 1998;17:831–839]. Next, an expectation maximization algorithm is then developed for determining the maximum likelihood estimates (MLEs) of the parameters of the model. In addition, we discuss the construction of confidence intervals for the parameters using the asymptotic distributions of the MLEs and the parametric bootstrap method, and assess their performance through a Monte Carlo simulation study. Finally, the proposed methodology was applied to a database on uterine cervical cancer.