嵌套病例对照研究中的两步估计方法(英文)

本文讨论嵌套病例对照研究中相对危险率的估计问题,引入了相对危险率的两步估计,并在一般嵌套病例对照抽样的假设下讨论了相对危险率的两步估计的相合性问题．最后给出了几个例子．     

利用配对的病例对照研究资料估计归因危险度比

本文介绍了利用１：１配对病例对照研究资料估计暴露的和整个靶人群的归因危险度比的方法。并对１９９０年宁波市江北区伤寒、副伤寒甲爆发流行期间进行的１：１配对病例对照调查资料，再次作了统计分析，结果满意，而且容易计算。最后对归因危险度比的流行病学意义进行了探讨。     

比例风险模型下病例队列设计中两种加权估计方法及其应用

对于大型队列研究或观察型研究,基于生存数据的病例队列设计是一种能有效节约成本和提高效率的抽样机制.这种抽样设计仅对一个随机抽取的子队列以及子队列之外所有经历了感兴趣事件的病例个体进行关键协变量的测量,具有显著的成本效益.本文研究如何应用比例风险模型拟合病例队列研究数据.探讨逆概率加权和与时间相关加权这两种基于加权估计方程的统计推断方法和其渐近性质等理论结果.通过一系列的统计模拟研究展示了病例队列设计的优良性以及相较于传统简单随机抽样设计的高效性.进一步,应用这两种推断方法分析了两个实际数据,展示了其在实际中的应用价值和前景.     

非参数回归函数之改良基于分割的估计的强相合性（英）

设(X,Y),(X1,Y1),…,(XnYn)为取值于 Rd× R的 i．i．d．随机变量,E(|Y|) ＜∞．设mn(x)为回归函数m(x)=E(|Y|X=x)基于分割的估计,本文在对mn(x)进行改良的条件下得到改良的基于分割的强相合估计．     

基于病例队列设计的平均处理效应的估计

病例队列设计因为具有成本效益而被广泛应用于流行病学和生物医学的研究中.对于病例队列设计,现有的统计方法主要集中在如何得到回归参数的相合及有效的估计上,然而很少有工作估计非随机化处理的因果效应.本文基于病例队列设计数据提出了一种有效的估计平均处理效应的方法,建立了所提估计量的相合性和渐近正态性,并通过仿真研究考察了其在有限样本下的表现.最后,我们将所提方法应用于真实数据的分析中.     

基于熵理论的病例父母亲对照研究来精细定位

原始的连锁不平衡熵指数通过比较群体样本中标记熵和条件熵来定位疾病位点或数量性状位点．它可能受群体混杂的影响．而利用病例父母亲对照研究或其他的家系研究可以避免群体混杂的影响．本文拓展了连锁不平衡熵指数到病例父母亲数据,将没有传递给受累子代的父母亲的基因型视为对照样本．随机模拟的结果表明连锁不平衡熵指数适用家系研究．     

病例队列研究下带约束的Cox模型中参数的一种加权估计方法

许多大型队列研究的主要预算和成本通常来自昂贵的关键协变量的采集与测量.在有限的预算或者时间下,观测大型队列中所有研究对象的昂贵协变量往往是不可行和低效的.因此,研究人员一直致力于寻找和使用能节约成本并能达到预设效率的抽样设计方法.对于生存数据,病例队列设计正是这样一种具有成本效益的有偏抽样机制.进一步,在病例队列研究中,为了利用更多的数据先验信息来提高研究的效率,可以在统计建模过程中对模型参数进行合理的假设和约束.本文研究病例队列设计下带约束的Cox模型中参数的估计方法.我们提出了一种加权约束估计的方法,并建立了所提出估计的渐近理论.发展了一种新的约束MM算法来实现所提出的加权约束估计的数值计算.通过统计模拟研究评估了所提出方法在有限样本量下的表现.分析了一个肾母细胞瘤的实际数据来展示所提出方法的实际应用价值.     

病例-对照研究中基因型不确定时单倍型关联分析的似然方法

从荧光强度数据出发研究疾病与单倍型之间的相关性.利用基于混合t分布的聚类算法得到了每个个体的所有可能的基因型("基因图谱"), 根据所有这些可能的基因型考虑基于单倍型的logistic回归模型,并且给出了一个研究疾病与单倍型之间相关性的似然方法, 通过进一步的模拟研究发现该似然方法减小了基因型测量误差给单倍型关联分析带来的影响.     

病例队列设计下加性风险回归分析及其在乳腺癌数据中的应用

本文研究了如何应用加性风险模型拟合由病例队列设计获取的生存数据的问题.利用参数的一种加权估计方法并综述其渐近性质.通过模拟研究获得了这种方法在有限样本量下的优良表现,并评估了病例队列设计相较于简单随机抽样设计的有效性.本文推广简单随机抽样至病例队列设计,并将此种方法应用于一个实际的乳腺癌数据,展示其在实际中的应用价值和...     

误差为MA（∞）序列的半参数回归模型的小波估计的渐近性质

本文研究误差为MA(∞)时间序列的半参数回归模型.利用小波方法,研究了参数分量β非参数分量g(t)的小波估计βn、gn(·)的渐近性质.在适当的条件下,得到了βn的渐近正态性、强收敛速度、矩收敛速度及gn(·)的强相合性和矩相合性.     

Exact asymptotic minimax constants for the estimation of analytical functions in L p

The L _p minimax risks (1≤p<∞) are studied for statistical estimation in the Gaussian white noise model. The asymptotic rate and constants are given, and the optimal estimator is proposed. This, together with the work of Golubev, Levit and Tsybakov (1996) establishes the classification of the L _p minimax constants on the classes of analytical functions. Received: 10 December 1996 / Revised version: 14 December 1997     

Uniform rates of convergence in the CLT for quadratic forms in multidimensional spaces

Summary.   Let X,X ₁,X ₂,… be a sequence of i.i.d. random vectors taking values in a d-dimensional real linear space ℝ ^d . Assume that E X=0 and that X is not concentrated in a proper subspace of ℝ ^d . Let G denote a mean zero Gaussian random vector with the same covariance operator as that of X. We investigate the distributions of non-degenerate quadratic forms ℚ[S _N ] of the normalized sums S _N =N ^−1/2(X ₁+⋯+X _N ) and show that

Functional centrality in graphs

In this article, we introduce the functional centrality as a generalization of the subgraph centrality. We propose a general method for characterizing nodes in the graph according to the number of closed walks starting and ending at the node. Closed walks are appropriately weighted according to the topological features that we need to measure.     

On the Sparsity Order of a Graph and Its Deficiency in Chordality

Given a graph G on n nodes, let denote the cone consisting of the positive semidefinite matrices (with real or complex entries) having a zero entry at every off-diagonal position corresponding to a non edge of G. Then, the sparsity order of G is defined as the maximum rank of a matrix lying on an extreme ray of the cone . It is known that the graphs with sparsity order 1 are the chordal graphs and a characterization of the graphs with sparsity order 2 is conjectured in [1] in the real case. We show in this paper the validity of this conjecture. Moreover, we characterize the graphs with sparsity order 2 in the complex case and we give a decomposition result for the graphs with sparsity order in both real and complex cases. As an application, these graphs can be recognized in polynomial time. We also indicate how an inequality from [17] relating the sparsity order of a graph and its minimum fill-in can be derived from a result concerning the dimension of the faces of the cone . Received August 31, 1998/Revised April 26, 2000     

Random Matchings in Regular Graphs

d -regular graph G, let M be chosen uniformly at random from the set of all matchings of G, and for let be the probability that M does not cover x. We show that for large d, the 's and the mean μ and variance of are determined to within small tolerances just by d and (in the case of μ and ) : Theorem. For any d-regular graph G, (a) , so that , (b) , where the rates of convergence depend only on d. Received: April 12, 1996     

On signature-based expressions of system reliability

The concept of signature was introduced by Samaniego for systems whose components have i.i.d. lifetimes. This concept proved to be useful in the analysis of theoretical behaviors of systems. In particular, it provides an interesting signature-based representation of the system reliability in terms of reliabilities of k-out-of-n systems. In the non-i.i.d. case, we show that, at any time, this representation still holds true for every coherent system if and only if the component states are exchangeable. We also discuss conditions for obtaining an alternative representation of the system reliability in which the signature is replaced by its non-i.i.d. extension. Finally, we discuss conditions for the system reliability to have both representations.     

On testing equality of pairwise rank correlations in a multivariate random vector

Spearman’s rank-correlation coefficient (also called Spearman’s rho) represents one of the best-known measures to quantify the degree of dependence between two random variables. As a copula-based dependence measure, it is invariant with respect to the distribution’s univariate marginal distribution functions. In this paper, we consider statistical tests for the hypothesis that all pairwise Spearman’s rank correlation coefficients in a multivariate random vector are equal. The tests are nonparametric and their asymptotic distributions are derived based on the asymptotic behavior of the empirical copula process. Only weak assumptions on the distribution function, such as continuity of the marginal distributions and continuous partial differentiability of the copula, are required for obtaining the results. A nonparametric bootstrap method is suggested for either estimating unknown parameters of the test statistics or for determining the associated critical values. We present a simulation study in order to investigate the power of the proposed tests. The results are compared to a classical parametric test for equal pairwise Pearson’s correlation coefficients in a multivariate random vector. The general setting also allows the derivation of a test for stochastic independence based on Spearman’s rho.     

An isoperimetric estimate and W^{1,p}-quasiconvexity in nonlinear elasticity

A class of stored energy densities that includes functions of the form with , g and h convex and smooth, and is considered. The main result shows that for each such W in this class there is a such that, if a 3 by 3 matrix satisfies , then W is -quasiconvex at on the restricted set of deformations that satisfy condition (INV) and a.e. (and hence that are one-to-one a.e.). Condition (INV) is (essentially) the requirement that be monotone in the sense of Lebesgue and that holes created in one part of the material not be filled by material from other parts. The key ingredient in the proof is an isoperimetric estimate that bounds the integral of the difference of the Jacobians of and by the -norm of the difference of their gradients. These results have application to the determination of lower bounds on critical cavitation loads in elastic solids. Received January 5, 1998 / Accepted March 13, 1998     

The fluctuations of the overlap in the Hopfield model with finitely many patterns at the critical temperature

We investigate the limiting fluctuations of the order parameter in the Hopfield model of spin glasses and neural networks with finitely many patterns at the critical temperature 1/β _c = 1. At the critical temperature, the measure-valued random variables given by the distribution of the appropriately scaled order parameter under the Gibbs measure converge weakly towards a random measure which is non-Gaussian in the sense that it is not given by a Dirac measure concentrated in a Gaussian distribution. This remains true in the case of β = β _N →β _c = 1 as N→∞ provided β _N converges to β _c = 1 fast enough, i.e., at speed ?(1/). The limiting distribution is explicitly given by its (random) density. Received: 12 May 1998 / Revised version: 14 October 1998