This paper provides an alternative proof of the derivation of the distribution of the largest eigenvalue of an elliptical Wishart matrix in contrast to the result of CaroLopera et al. (2016). We show the relation between multivariate and matrix-variate t distributions. From this relation, we can generate random numbers drawn from the matrix-variate t distribution. A Monte Carlo simulation is conducted to evaluate the accuracy for the truncated distribution function of the largest eigenvalue of the elliptical Wishart matrix. Exact computation of the distribution of the smallest eigenvalue is also presented.
We aim at improving the accuracy of indoor position estimation through a statistical approach. In this study, we propose a position estimation method based on Time-of-Arrival (ToA). ToA data are often useful. However, ToA data include a positive bias due to the reflection of radio waves. Therefore, it is difficult to estimate the TAG position from ToA data directly without an accurate bias correction. In this paper, we propose a maximum likelihood estimation method for the TAG position using gamma regression and a rotated distribution, and we show that the estimation with bias correction is more accurate than the estimation without bias correction. In addition,we show that our method also provides a confidence region for the TAG position.
The cone-convex hull by complement (ccc-hull) is a generalized convex hull created from Poincare Cones. We propose a new approach with the ccc-hull for the simulation of the extent of damage by a tsunami, and simulate the damaged area at the time of the Great East Japan Earthquake for approximate damage by samples from a twodimensional Non-homogeneous Poisson Process. Then, we consider the problem of the estimation of the parameter, which corresponds to the opening angle of the Poincare Cones. We believe our suggestion can be used to predict the extent of a tsunami in a specified area in Japan.
A simple method is presented to enhance statistical power of score tests for regression models via Fisher transformation (or Fisher’s z-transformation) by exploiting a relationship with the partial correlation coefficient. Simulation studies mimicking marginal association and gene-environment interaction analyses for genome-wide association studies (GWASs) under case-control design demonstrate that the Fisher transformation enhances power of the score tests while maintaining type I error asymptotically. The smaller the sample size is, the more the enhancement is pronounced, at the expense of inflated type I error due to invalidating asymptotic approximation. Accordingly, the proposed method may be applied when sample size is enough for valid asymptotic approximation. An illustration with real GWAS data is also presented.
Many observations tend to concentrate in the main diagonal cells when analyzing square contingency tables with ordered categories. Although many statisticians have proposed a variety of symmetry and asymmetry models, constraints on the main diagonal cells are not considered. This implies that the observed frequencies on the main diagonal cells are not utilized. Herein we propose three models that indicate an asymmetric structure for the log odds ratio for cell probabilities. These models constrain the main diagonal cells such that the information in the main diagonal cells can be utilized. Then we decompose the symmetry model using the proposed models.
The performance of randomization methods in consideration of the impact of a prognostic factor that has an interaction and baseline characteristics that have no effect on the outcome has not been clarified, especially for small sized clinical trials. We conducted numerical simulations to identify the difference in behaviour of the empirical power and the empirical type 1 error rate among some randomization methods and statistical analyses when we use a prognostic factor that has an interaction or baseline characteristics that have no effect on the outcome for small sized randomized controlled trials. The empirical power was higher when using a prognostic factor that had an interaction. Also, by using stratified blocked randomization (ST) or minimization (MI) with the multiple regression, the empirical power was further increased. On the other hand, the empirical power was lower when using baseline characteristics that had no effect on the outcome. We recommend conducting ST or MI, multiple regression and using a prognostic factor that has an interaction in small-size randomized controlled trials.