查看更多>>摘要：A general linear hypothesis testing (GLHT) problem in heteroscedastic one-way MANOVA for high-dimensional data is considered and a normal reference L-2-norm based test for the problem is proposed. Different from a few existing methodologies on the GLHT problem which impose strong assumptions on the underlying covariance matrices so that the associated tests' null distributions are asymptotically normal, it is shown that under some regularity conditions, the proposed test statistic under the null hypothesis and a chi-square type mixture have the same normal or non-normal limiting distributions. It is then suggested to approximate the test's null distribution using the distribution of the chi-square type mixture, which can be further approximated by the Welch- Satterthwaite chi-square-approximation with approximation parameters consistently estimated. Several simulation studies and a real data application are presented to demonstrate the good performance of the proposed test. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：The investigation of the relationship between a time-to-event outcome and time dependent risk factors is often of great interest in longitudinal studies. However, the time-dependent risk factors may not be directly observed or simply measured by a single variable. Instead, they are latent and should be characterized by several observed variables from different aspects. In this article, we consider a novel joint modeling framework to examine the effects of latent time-dependent risk factors on the hazard of interest. A factor analysis model is used to depict the dependence between time dependent latent variables and multivariate longitudinal observed variables, and a proportional hazard model is adopted for linking latent time-dependent factors to the hazard of interest. We develop a hybrid procedure that combines an asymptotically distribution-free generalized least square approach and a conditional score method. Theoretical results are provided on the consistency and asymptotic normality of parameter estimators. The method is evaluated through simulation studies and applied to a dataset about Alzheimer's disease. (c) 2021 Elsevier Inc. All rights reserved.
查看更多>>摘要：We study theoretically, for the first time, the Dirichlet kernel estimator introduced by Aitchison and Lauder (1985) for the estimation of multivariate densities supported on the d-dimensional simplex. The simplex is an important case as it is the natural domain of compositional data and has been neglected in the literature on asymmetric kernels. The Dirichlet kernel estimator, which generalizes the (non-modified) unidimensional Beta kernel estimator from Chen (1999), is free of boundary bias and non-negative everywhere on the simplex. We show that it achieves the optimal convergence rate O(n(-4/(d+4))) for the mean squared error and the mean integrated squared error, we prove its asymptotic normality and uniform strong consistency, and we also find an asymptotic expression for the mean integrated absolute error. To illustrate the Dirichlet kernel method and its favorable boundary properties, we present a case study on minerals processing. (c) 2021 Elsevier Inc. All rights reserved.
NSTL
Elsevier