基于因变量抽样设计下线性回归模型的假设检验问题

在许多大型队列研究中,采用节约成本并能提高效率的抽样机制至关重要,基于因变量的抽样设计正是这样一种有偏抽样机制.这种方法最大的优点在于:能够将资源集中在那些包含有更多的协变量与因变量关系信息的研究群体上.本文研究基于因变量抽样设计下的线性模型中回归方程显著性检验以及回归系数显著性检验问题.基于一种半参数经验轮廓似然的方法,我们分别为回归方程检验与回归系数检验提出了相应的检验统计量,获得了所提出检验统计量的渐近性质.通过模拟研究评估了所提出的检验方法在有限样本下的表现,并应用提出的方法分析了一个孕妇分娩的实际数据.     

A Semiparametric Two-Sample Hypothesis Testing Problem for Random Graphs

Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning. In this article, we consider a semiparametric problem of two-sample hypothesis testing for a class of latent position random graphs. We formulate a notion of consistency in this context and propose a valid test for the hypothesis that two finite-dimensional random dot product graphs on a common vertex set have the same generating latent positions or have generating latent positions that are scaled or diagonal transformations of one another. Our test statistic is a function of a spectral decomposition of the adjacency matrix for each graph and our test procedure is consistent across a broad range of alternatives. We apply our test procedure to real biological data: in a test-retest dataset of neural connectome graphs, we are able to distinguish between scans from different subjects; and in the C. elegans connectome, we are able to distinguish between chemical and electrical networks. The latter example is a concrete demonstration that our test can have power even for small-sample sizes. We conclude by discussing the relationship between our test procedure and generalized likelihood ratio tests. Supplementary materials for this article are available online.     

线性度量误差模型的序列相关检验

回归模型的序列相关检验是经济和金融数据分析中的一项重要的工作.基于最小二乘残差,作者提出了一个检验统计量以检验线性度量误差模型的误差序列是否存在序列相关性.在零假设下,得到了检验统计量的渐近分布.数值模拟结果表明,这里提出的检验统计量具有良好的有限样本性质.     

A Completeness Problem Related to the Riemann Hypothesis

It is proven that the set of eigenvectors and generalized eigenvectors associated to the non-zero eigenvalues of the Hilbert-Schmidt (non nuclear, non normal) integral operator on L²(0, 1)

A Decision Model for a Sequential Testing Problem in civil Engineering

A sequential decision problem in civil engineering is formulatedas a dynamic programming model. A set of theorems lead to amore efficient formulation, permitting the solution routineto be programmed on a microcomputer. The solution is printedin table fonn, directly providing a decision rule usable bythe foreman in the field. The paper illustrates a point whichis becoming increasingly apparent: the power and availabilityof portable computer systems are making many decision problemsamenable to on-site analysis using models based upon rigoroustheory.     

一类马氏样本下假设检验问题错误概率的估计

本文考虑样本不独立情形的统计推断问题,研究基于马氏样本的最优势检验,给出了此情形的Neyman-Pearson基本引理.当样本容易足够大时,利用大偏差原理,得到了Neyman-Pearson型检验所犯两类错误概率的精确估计,它推广了经典Neyman-Pearson基本引理的相关结果.     

有整数限制的运输问题

经典的运输问题是一个线性规划模型。本文讨论了把产地运输到销地的物资数量限制为非负整数时的运输问题，从理论上证明了这种有整数限制的运输问题模型可以转化为相应的线性规划模型来求解，有效地降低了计算难度。     

TIME-EXTRAPOLATION ALGORITHM （TEA） FOR LINEAR PARABOLIC PROBLEMS

The fast solutions of Crank-Nicolson scheme on quasi-uniform mesh for parabolic prob- lems are discussed. First, to decrease regularity requirements of solutions, some new error estimates are proved. Second, we analyze the two characteristics of parabolic discrete scheme, and find that the efficiency of Multigrid Method （MG） is greatly reduced. Nu- merical experiments compare the efficiency of Direct Conjugate Gradient Method （DCG） and Extrapolation Cascadic Multigrid Method （EXCMG）. Last, we propose a Time- Extrapolation Algorithm （TEA）, which takes a linear combination of previous several level solutions as good initial values to accelerate the rate of convergence. Some typical extrapolation formulas are compared numerically. And we find that under certain accuracy requirement, the CG iteration count for the 3-order and 7-level extrapolation formula is about 1/3 of that of DCG＇s. Since the TEA algorithm is independent of the space dimension, it is still valid for quasi-uniform meshes. As only the finest grid is needed, the proposed method is regarded very effective for nonlinear parabolic problems.     

部分线性模型中的非参数部分的线性性检验

In this paper,we propose the test statistic to check whether the nonpara- metric function in partially linear models is linear or not.We estimate the nonpara- metric function in alternative by using the local linear method,and then estimate the parameters by the two stage method.The test statistic under the null hypothesis is calculated,and it is shown to be asymptotically normal.     

On Testing Variance Components in Unbalanced Mixed Linear Model

The paper presents some approximate and exact tests for testing variance components in general unbalanced mixed linear model. It extends the results presented by Seifert (1992) with emphasis on the computational aspects of the problem.     

一元线性回归检验理论的一种证明

利用正交变换法,给出一元线性回归假设检验定理的一种直接证明.这种证明方法可供在数理统计教学中作参考.     

A Problem in Linear Matrix Approximation

Let A be a normal operator in ??(H), H a complex Hilbert space, and let ? _A = ? {AX - XA:X ∈ ??(H)} be the commutator subspace of ??(H) associated with A. If B in ??(H) commutes with A, then B is orthogonal to ?_A with respect to the spectral norm; i.e., the null operator is an element of best approximation of B in ? _A. This was proved by J. Anderson in 1973 and extended by P. J. Maher with respect to the Schatten p-norm recently. We take a look at their result from a more approximation theoretical point of view in the finite dimensional setting; in particular, we characterize all elements of best approximation of B in R_A and prove that the metric projection of H onto ?_A is continuous.     

Clifforrd分析中广义双正则函数的(线性)非线性边值问题

本文研究Ｃｌｉｆｏｒｄ分析中广义双正则函数的一个非线性边值问题：Ａ（ｔ１，ｔ２）Ｗ＋＋（ｔ１，ｔ２）＋Ｂ（ｔ１，ｔ２）Ｗ＋－（ｔ１，ｔ２）＋Ｃ（ｔ１，ｔ２）Ｗ－＋（ｔ１，ｔ２）＋Ｄ（ｔ１，ｔ２）Ｗ－－（ｔ１，ｔ２）＝ｇ（ｔ１，ｔ２）ｆｔ１，ｔ２，Ｗ＋＋（ｔ１，ｔ２），Ｗ＋－（ｔ１，ｔ２），Ｗ－＋（ｔ１，ｔ２），Ｗ－－（ｔ１，ｔ２）［］．先讨论解的积分表示式，再研究几个奇异算子，最后用Ｓｃｈａｕｄｅｒ不动点原理（压缩映射定理）证明了解的存在性（唯一性）．目前还没有见到其它国内外学者研究广义双正则函数的非线性边值问题．本文推广了Ｆ．Ｂｒａｃｋｓ，Ｗ．Ｐｉｎｃｋｅｔ［１０］，ＬｅＨｕａｎｇ Ｓｏｎ［１１］，Ｒ．Ｐ．ＧｉｌｂｅｒｔａｎｄＪ．Ｌ．Ｂｕｃｈｎａｎ［１５］和黄沙［１３］的工作     

A Statistic for Testing the Null Hypothesis of Elliptical Symmetry

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of ^d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.     

Almost Periodic Linear System and Exponential Dichotomies (in English)

本文讨论概周期线性系统具有指数型二分法和它的特征指数的关系。 考虑线性系统 $\[\frac{{dx}}{{dt}} = A(t)x\]$ （1） 其中A(t)是n*n方阵，它在实轴上连续和有界。如果（1）有基本方阵X(t)，具有如下的分解 $\[X(t) = {X_1}(t) + {X_2}(t),{X^{ - 1}}(s) = {Z_1}(s) + {Z_2}(s)\]$ $\[X(t){X^{ - 1}}(s) = {X_1}(t){Z_1}(s) + {X_2}(t){Z_2}(s)\]$ 同时有常数 \alpha ,\beta >0,使 $\[||{X_1}(t){Z_1}(s)|| \le \beta exp( - \alpha (t - s)),t \ge s\]$ $\[||{X_2}(t){Z_2}(s)|| \le \beta exp(\alpha (t - s)),s \ge t\]$ 就说（1）具有指数型二分法。 我们所得的结果，可叙述如下： 一、对拟周期线性系统，存在同频率的酉变换，把它化为三角型系统。从而推出： 若拟周期线性系统的特征指数异于零，则它具有指数型二分法。 二、对概周期线性系统，定了广义的零特征指数。当它不具有广义的零特征指数，则该系统具有指数型二分法。 三、利用一和二的结果，解决了Hale所提的关于中心积分流形的存在性问题。     

假设检验中的原假设选取问题

针对假设检验中"对一个具体问题,在相同的显著性水平α下进行假设检验,如果交换原假设和备择假设,得到的结论可能完全相反"这一问题进行分析,并给出根据实际问题的要求如何正确建立原假设和备择假设的方法.     

Testing the Gumbel Hypothesis Via the Pot-Method

We consider an i.i.d. sample, generated by some distribution function, which belongs to the domain of attraction of an extreme value distribution with unknown shape and scale parameters. We treat the scale parameter as a nuisance parameter and establish for the hypothesis of Gumbel domain of attraction an asymptotically optimal test based on those observations among the sample, which exceed a given threshold sequence. Asymptotic optimality is achieved along certain contiguous extreme value alternatives within the concept of local asymptotic normality (LAN). Adaptive test procedures exist under restrictive assumptions. The finite sample size behavior of the proposed test is studied by simulations and it is compared to that of a test based on the sample coefficient of variation.     

P*(κ)阵线性互补问题一种新的宽邻域预估-校正内点算法

基于邻近度量函数的最小值,对P*(κ)阵线性互补问题提出了一种新的宽邻域预估-校正算法,在较一般的条件下,证明了算法的迭代复杂性为O(κ+1)23n log(x0ε)Ts0.算法既可视为Miao的P*(κ)阵线性互补问题Mizuno-Todd-Ye预估-校正内点算法的一种变形,也可以视为最近Zhao提出的线性规划基于邻近度量函数最小值的宽邻域内点算法的推广.     

连续型半参数广义线性纵向数据模型的方差成分检验

回归模型的方差成分检验是一个非常重要的问题.该文针对离差参数的变异, 随机效应的影响及两者同时具有的三种情形, 研究了基于纵向数据的连续型半参数广义线性模型的方差成分检验, 得到了Score检验统计量, 最后通过计算机模拟验证了该文所提出的方法的有效性.