A hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendations are made based on their type I error probabilities and powers. Finally, all mentioned tests are applied to a real data example.

Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendationsare made based on their type I error probabilities and powers. Finally, all mentioned tests areapplied to a real data example.

In this paper, we study a Kronecker structured model for covariance matrices when data are matrix-valued. Using the modified Cholesky decomposition for Kronecker structured covariance matrix, we propose a regularized covariance estimator by imposing shrinkage and smoothing penalties on the Cholesky factors. A regularized flip-flop (RFF) algorithm is developed to produce a statistically efficient estimator for a large covariance matrix of matrix-valued data. Asymptotic properties are investigated and the performance of the estimator is evaluated by simulations. The results presented are applied to real data example.

We extend the existing family of flexible survival models by assembling models scattered across the literature into a more knit form and under the same umbrella. New special cases are obtained not only by constraining the shape and scale parameters of the extended generalized gamma (EGG) model to fixed constants, but also by imposing relationships (such as equality, reciprocal, and negative reciprocal) between them. Apart from common parametric distributions such as exponential, Weibull, gamma, and log normal, the further extended family includes Rayleigh, inverse Rayleigh, ammag, inverse ammag, and half-normal distributions. The models are applied, in a Bayesian framework, on time to entry into first marriage among Eritrean men and women based on data from the 2010 Population and Health Survey. The application demonstrates that the further extended family of distributions provides a wide range of alternatives for a baseline distribution in the analysis of survival data. The empirical results reveal that the inverse gamma model fits best the data for men. It also performs closely as good as the EGG model in the data for women as well as in the combined sample.

In this article, we address the problem of simultaneous testing hypothesis about mean and covariance matrix for repeated measures data when both the mean vector and covariance matrix are patterned. In particular, tests about the mean vector under block circular and doubly exchangeable covariance structures have been considered. The null distributions are established for the corresponding likelihood ratio test statistics, and expressions for the exact or near-exact probability density and cumulative distribution functions are obtained. The application of the results is illustrated by both a simulation study and a real-life data example.

Estimating inverse covariance matrix is an essential part of many statistical methods. This paper proposes a regularized estimator for the inverse covariance matrix. Modified Cholesky decomposition (MCD) is utilized to construct positive definite estimators. Instead of directly regularizing the inverse covariance matrix itself, we impose regularization on the Cholesky factor. The estimated inverse covariance matrix is used to build Mahalanobis distance (MD). The proposed method is evaluated by detecting outliers through simulations and empirical studies.

Objectives This study psychometrically evaluated GeneralSelf-Efficacy (GSE) Scale in patients planned for bariatricsurgery in Sweden.Design A cross-sectional psychometric study. Thepsychometric evaluation was guided by the COnsensus-based Standards for the selection of health statusMeasurement Instruments checklist for health-relatedreported-patient outcomes.Setting Three bariatric centres in Sweden.Participants Adult patients≥18 years old scheduled forprimary bariatric surgery (with sleeve gastrectomy orRoux-en-Y gastric bypass).Primary and secondary measures Psychometricproperties of the GSE.Results In total, 704 patients were included in theanalysis. Mean values for GSE items were 2.9–3.4 and themean GSE sum score was 31.4 (SD 4.7). There were nofloor or ceiling effects. Cronbach’s alpha was 0.89. Menreported a higher mean GSE than did women, that is, 31.2(SD 4.8) for women versus 32.1 (SD 4.3) for men, p=0.03.Correlation coefficients were weak or negligible: GSE andmental component summary score of 36-Item Short FormHealth Survey (SF-36)/RAND 36, r=0.18 (p<0.00); GSEand physical component summary score of SF-36/RAND36, r=0.07 (p=0.138); GSE and obesity- related problemscale r=−0.15 (p=0.001) and GSE and level of education,r=0.04 (p=0.35). Confirmatory factor analysis indicateda one-factor construct with a satisfactory goodness of fit,that is, Comparative Fit Index=0.927, root mean squareerror of approximation=0.092 and standardised root meansquare residual=0.045. The factor GSE explained almosthalf or over half of the variance of each item (0.45–0.75,p-values<0.001).Conclusions The GSE scale is a valid and reliable scalethat can be used to assess general self-efficacy in patientsundergoing bariatric surgery.

In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c=p/n→∞. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F=S−12S1—the product of a sample covariance matrix S1 (from the independent variable array (be(Zi)1×n) with the inverse of another covariance matrix S2 (from the independent variable array (Zj≠i)p×n)—are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S1 and S2 of the F-matrix is not required.

Models that capture symmetries present in the data have been widely used in different applications, with early examples from psychometric and medical research. The aim of this article is to study a random effects model focusing on the covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.