协变量维数可以趋于无穷的纵向数据的广义估计方程分析

广义估计方程(GEE)是分析纵向数据的常用方法.Balan,Schiopu-Kratina(2005)研究了协变量维数固定,GEE估计的渐近正态性.WANG(2011)研究了协变量维数趋于无穷,GEE估计的渐近正态性和响应变量是两点分布Wald统计量的渐近分布.本文证明协变量维数是固定的或趋于无穷,响应变量是任意分布的Wald统计量的渐近分布是卡方分布,Wald统计量可以直接用于统计推断.     

二次型在经济管理中的应用简介

本文是二次型及其定性理论在经济管理中的一些应用的归纳总结,包括多元函数极值存在的充分条件、线性回归模型中参数估计的最小二乘法、随机向量及其线性函数的数字特征、线性组合预测模型的误差平方和以及线性组合投资收益率的方差（风险）等。     

Equivalence of kinetic-theory and random-matrix approaches to Lyapunov spectra of hard-sphere systems

In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute values exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical approaches to these exponents so far can be divided into two groups, macroscopically oriented approaches, using kinetic theory or hydrodynamics, and more microscopically oriented random-matrix approaches in quasi-one-dimensional systems. In this paper, I present an approach using random matrices and weak-disorder expansion in an arbitrary number of dimensions. Correlations between subsequent collisions of a particle are taken into account. It is shown that the results are identical to those of a previous approach based on an extended Enskog equation. I conclude that each approach has its merits, and provides different insights into the approximations made, which include the Stoßzahlansatz, the continuum limit, and the long wavelength approximation. The comparison also gives insight into possible connections between Lyapunov exponents and fluctuations.     

Design of RLS Wiener estimators from randomly delayed observations in linear discrete-time stochastic systems

This paper presents the design of a new recursive least-squares (RLS) Wiener filter and fixed-point smoother based on randomly delayed observed values by one sampling time in linear discrete-time wide-sense stationary stochastic systems. The mixed observed value y(k) consists of the past observed value by one sampling time with the probability p(k) and of the current observed value at time k with the probability 1 − p(k). It is assumed that the delayed measurements are characterized by Bernoulli random variables. The observation is given as the sum of the signal z(k) and the white observation noise v(k). The RLS Wiener estimators explicitly require the following information: (a) the system matrix for the state vector; (b) the observation matrix; (c) the variance of the state vector; (d) the delayed probability p(k); (e) the variance of white observation noise v(k).     

IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.     

Semismooth Newton Coordinate Descent Algorithm for Elastic-Net Penalized Huber Loss Regression and Quantile Regression

We propose an algorithm, semismooth Newton coordinate descent (SNCD), for the elastic-net penalized Huber loss regression and quantile regression in high dimensional settings. Unlike existing coordinate descent type algorithms, the SNCD updates a regression coefficient and its corresponding subgradient simultaneously in each iteration. It combines the strengths of the coordinate descent and the semismooth Newton algorithm, and effectively solves the computational challenges posed by dimensionality and nonsmoothness. We establish the convergence properties of the algorithm. In addition, we present an adaptive version of the “strong rule” for screening predictors to gain extra efficiency. Through numerical experiments, we demonstrate that the proposed algorithm is very efficient and scalable to ultrahigh dimensions. We illustrate the application via a real data example. Supplementary materials for this article are available online.     

Regularized Estimation of Piecewise Constant Gaussian Graphical Models: The Group-Fused Graphical Lasso

The time-evolving precision matrix of a piecewise-constant Gaussian graphical model encodes the dynamic conditional dependency structure of a multivariate time-series. Traditionally, graphical models are estimated under the assumption that data are drawn identically from a generating distribution. Introducing sparsity and sparse-difference inducing priors, we relax these assumptions and propose a novel regularized M-estimator to jointly estimate both the graph and changepoint structure. The resulting estimator possesses the ability to therefore favor sparse dependency structures and/or smoothly evolving graph structures, as required. Moreover, our approach extends current methods to allow estimation of changepoints that are grouped across multiple dependencies in a system. An efficient algorithm for estimating structure is proposed. We study the empirical recovery properties in a synthetic setting. The qualitative effect of grouped changepoint estimation is then demonstrated by applying the method on a genetic time-course dataset. Supplementary material for this article is available online.     

基于岭回归和SVM的高维特征选择与肽QSAR建模

岭回归估计权重绝对值在一定程度上体现了对应特征作用大小, 据此发展了基于岭回归(RR)和支持向量机(SVM)的高维特征选择算法. 对苦味二肽(BTT)和细胞毒性T淋巴细胞(CTL)表位9 肽两个肽体系, 以氨基酸的531 个物理化学性质参数直接表征肽结构, 各获得1062、4779 个初始特征; 对训练集, 初始特征以岭回归排序后序贯引入, 当SVM留一法交叉测试(LOOCV)的均方误差(MSE)显著上扬时终止, 最后以多轮末尾淘汰进一步精筛, 分别获得7、18个物理化学意义明确的保留特征. 基于保留特征与支持向量回归(SVR), 对训练集建立定量构效关系(QSAR)模型, 预测独立测试集, 其拟合精度、留一法交叉测试精度、独立预测精度均优于现有文献报道结果. 新方法运行速度快, 选取的特征物理化学意义明确, 解释性强, 在肽、蛋白质定量构效关系建模等高维数据回归预测领域有较广泛应用前景.