Improved approximations to distributions of the largest and the smallest latent roots of a wishart matrix

Summary Normalizing transformations of the largest and the smallest latent roots of a sample covariance matrix in a normal sample are obtained, when the corresponding population roots are simple. Using our results, confidence intervals for population roots may easily be constructed. Some numerical comparisons of the resulting approximations are made in a bivariate case, based on exact values of the probability integral of latent roots.     

Exact Connections between Current Fluctuations and the Second Class Particle in a Class of Deposition Models

We consider a large class of nearest neighbor attractive stochastic interacting systems that includes the asymmetric simple exclusion, zero range, bricklayers’ and the symmetric K-exclusion processes. We provide exact formulas that connect particle flux (or surface growth) fluctuations to the two-point function of the process and to the motion of the second class particle. Such connections have only been available for simple exclusion where they were of great use in particle current fluctuation investigations. MSC: 60K35, 82C41     

Rate of growth of the coalescent set in a coalescing stochastic flow

Consider an isotropic stochastic flow in R_d (i.e. a simultaneous random, correlated motion of all points in space), where d=l,2 or 3, such that the joint law of the motion of two particles allows the particles to meet and coalesce in finite time. The coalescent set J _t is a random subset of R_d consisting of the initial positions of particles which have coalesced by time t with the particle which started at 0. We show that the expected volume of J t grows at a rate proportional to when d=1, and at rates close to proportional to t/log t (resp. t) when d = 2 (resp. d=3). We give an example of a coalescing stochastic flow when d = 3. These results are analogous to growth rates of expected population size of a surviving type in the "invasion process" described by Clifford and Sudbury     

Ridge Fusion in Statistical Learning

This article proposes a penalized likelihood method to jointly estimate multiple precision matrices for use in quadratic discriminant analysis (QDA) and model-based clustering. We use a ridge penalty and a ridge fusion penalty to introduce shrinkage and promote similarity between precision matrix estimates. We use blockwise coordinate descent for optimization, and validation likelihood is used for tuning parameter selection. Our method is applied in QDA and semi-supervised model-based clustering.     

Residual water suppression by indirect covariance NMR

Residual water solvent signals in 2D NMR experiments adversely affect appearance and subsequent analysis of spectra. A method for water suppression that is based on indirect covariance processing is described. It produces a symmetric spectrum with a water signal that is substantially decreased or completely absent. The method, which can be combined with other water suppression schemes, is demonstrated for 2D TOCSY, NOESY, and ROESY spectra of the protein, ubiquitin in aqueous solution.     

马氏距离聚类分析中协方差矩阵估算的改进

本文考虑了变量权重和样本类别的影响,建立了马氏距离聚类过程中评估协方差矩阵的迭代法。以Fisher的iris数据为样本,运用欧氏距离一般聚类、主成分聚类、改进前后的马氏距离聚类方法,进行实证分析和比较,结果表明本文所提出的新方法准确率至少提高了6.63%。最后,运用该方法对35个国家的相关指标数据进行聚类分析,确定了各国的卫生保健状况等级。     

均值方差结构模型的渐近稳健推断(英文)

均值方差模型广泛应用于行为、教育、医学、社会和心理学的研究.经典的极大似然估计对于异常点和分布扰动易受影响.本文基于目标函数最小化给出稳健估计,并基于稳健偏差提出模型拟合.     

Statistical comparison of the slopes of two regression lines: A tutorial

Comparing the slopes of two regression lines is an almost daily task in analytical laboratories. The usual procedure is based on a Student’s t-test although literature differs in whether the standard errors of the slopes or the standard errors of the regressions should be employed to get a pooled standard error. In this work fundamental concepts on the use of the Student’s test were reviewed and Monte Carlo simulations were done to ascertain whether relevant differences arise when the two options are considered. It was concluded that for small sample sets (as it is usual in analytical laboratories) the Student’s t-test based on the standard error of regression models must be used and special attention must be paid on the equality of the models variances. Finally, alternative approaches were reviewed, with emphasis on a simple one based on the analysis of the covariance (ANCOVA).     

Using indirect covariance spectra to identify artifact responses in unsymmetrical indirect covariance calculated spectra

Several groups of authors have reported studies in the areas of indirect and unsymmetrical indirect covariance NMR processing methods. Efforts have recently focused on the use of unsymmetrical indirect covariance processing methods to combine various discrete two-dimensional NMR spectra to afford the equivalent of the much less sensitive hyphenated 2D NMR experiments, for example indirect covariance (icv)-heteronuclear single quantum coherence (HSQC)-COSY and icv-HSQC-nuclear Overhauser effect spectroscopy (NOESY). Alternatively, unsymmetrical indirect covariance processing methods can be used to combine multiple heteronuclear 2D spectra to afford icv-13C-15N HSQC-HMBC correlation spectra. We now report the use of responses contained in indirect covariance processed HSQC spectra as a means for the identification of artifacts in both indirect covariance and unsymmetrical indirect covariance processed 2D NMR spectra.