Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems

The purpose of this paper is to derive, in a unified way, second order necessary and sufficient optimality criteria, for four types of nonsmooth minimization problems: thediscrete minimax problem, thediscrete l ₁-approximation, the minimization of theexact penalty function and the minimization of theclassical exterior penalty function. Our results correct and supplement conditions obtained by various authors in recent papers.     

Nonnull distribution of likelihood ratio criterion for reality of covariance matrix

In this paper the distribution of the likelihood ratio test for testing the reality of the covariance matrix of a complex multivariate normal distribution is investigated. Some simplifications in the noncentral distribution are made and the noncentral distribution is derived for the special case where the rank of the noncentrality matrix is two. In the null case exact expressions for the distribution are given up to p = 6, and percentage points are tabulated. These percentage points were compared with percentage points derived from an asymptotic expansion of the distribution, and the accuracy of the approximation was found to be sufficient for several practical situations.     

On the Law of The Iterated Logarithm for Rapidly Increasing Subsequences

The usual law of the iterated logarithm states that the partial sums S_n of independent and identically distributed random variables can be normalized by the sequence a_n = √nlog log n, such that limsup_n→∞ S_n/a_n = √2 a.s. As has been pointed out by Gut (1986) the law fails if one considers the limsup along subsequences which increase faster than exponentially. In particular, for very rapidly increasing subsequences {n_k≥1} one has limsup_k→∞ S_nk/a_nk = 0 a.s. In these cases the normalizing constants a_nk have to be replaced by √nk log k to obtain a non-trivial limiting behaviour: limsup_k→∞ S_nk/ √nk log k = √2 a.s. We will present an intelligible argument for this structural change and apply it to related results.     

非线性均值方差模型的贝叶斯数据删除统计诊断

文章在非线性均值方差模型框架下基于K-L距离研究贝叶斯数据删除影响的统计诊断问题,通过应用Gibbs抽样和MH算法估计贝叶斯数据删除影响诊断统计量.随机模拟研究和红鳟鲑鱼数据的数值例子说明该诊断方法的可行性.     

Penalized Orthogonal Iteration for Sparse Estimation of Generalized Eigenvalue Problem

We propose a new algorithm for sparse estimation of eigenvectors in generalized eigenvalue problems (GEPs). The GEP arises in a number of modern data-analytic situations and statistical methods, including principal component analysis (PCA), multiclass linear discriminant analysis (LDA), canonical correlation analysis (CCA), sufficient dimension reduction (SDR), and invariant co-ordinate selection. We propose to modify the standard generalized orthogonal iteration with a sparsity-inducing penalty for the eigenvectors. To achieve this goal, we generalize the equation-solving step of orthogonal iteration to a penalized convex optimization problem. The resulting algorithm, called penalized orthogonal iteration, provides accurate estimation of the true eigenspace, when it is sparse. Also proposed is a computationally more efficient alternative, which works well for PCA and LDA problems. Numerical studies reveal that the proposed algorithms are competitive, and that our tuning procedure works well. We demonstrate applications of the proposed algorithm to obtain sparse estimates for PCA, multiclass LDA, CCA, and SDR. Supplementary materials for this article are available online.     

A Dual Dynamic Programming for Multidimensional Elliptic Optimal Control Problems

This paper deals with the optimal control problems with multiple integrals and an elliptic partial differential equation. The sufficient conditions for optimality in these problems are proved through a dual dynamic programming. The concept of an optimal dual feedback is introduced, and the theorem guaranteeing its existence is established. For the purposes of numerical methods, the ε-version of the verification theorem provided appears to be very useful.     

改进的基于主成分分析的三维人脸形状建模

针对基于主成分分析(PCA)的三维(3D)人脸形状重构不精确的缺点,对位移向量、缩放因子、旋转矩阵、重构系数等参数进行了精确的定义和计算,并对重构模型进行了有效的调整。根据CVL Face Database建立了113个3D人脸形状模型,经迭代运算后重构出了由特征点组成的稀疏3D人脸形状模型。利用径向基函数(RBF)得到了密集3D人脸形状模型。试验结果表明,算法可以得到精确的重构模型,对深度旋转的人脸图像和特征点定位误差也有很好的鲁棒性。     

Stability criteria for certain high even order delay differential equations

In this paper we study the asymptotic stability of the zero solution of even order linear delay differential equations of the form