自组网可靠性评价方法

网络可靠性是网络性能评估指标的一个方面,对于网络系统级的性能评估有重要意义。该文通过构建随时间变化的表征网络节点连通性状态的关联矩阵,在节点故障和移动性变化的情况下,对自组网网络可靠性进行了研究,提供了一种自组网可靠性定量评价方法。通过大量的随机试验表明,该方法能有效验证自组网的可靠性。     

Structure Prediction and Computation of Sparse Matrix Products

We consider1 the problem of predicting the nonzero structure of a product of two or more matrices. Prior knowledge of the nonzero structure can be applied to optimize memory allocation and to determine the optimal multiplication order for a chain product of sparse matrices. We adapt a recent algorithm by the author and show that the essence of the nonzero structure and hence, a near-optimal order of multiplications, can be determined in near-linear time in the number of nonzero entries, which is much smaller than the time required for the multiplications. An experimental evaluation of the algorithm demonstrates that it is practical for matrices of order 103 with 104 nonzeros (or larger). A relatively small pre-computation results in a large time saved in the computation-intensive multiplication.     

Estimating age-specific incidence of dementia using prevalent cohort data

In prospective cohort studies, individuals are usually recruited according to a certain cross-sectional sampling criterion. The prevalent cohort is defined as a group of individuals who are alive but possibly with disease at the beginning of the study. It is appealing to incorporate the prevalent cases to estimate the incidence rate of disease before the enrollment. The method of back calculation of incidence rate has been used to estimate the incubation time from human immunodeficiency virus (HIV) infection to AIDS. The time origin is defined as the time of HIV infection. In aging cohort studies, the primary time scale is age of disease onset, subjects have to survive certain years to be enrolled into the study, thus creating left truncation (delay entry). The current methods usually assume that either the disease incidence is rare or the excess mortality due to disease is small compared with the healthy subjects. So far the validity of the results based on these assumptions has not been examined. In this paper, a simple alternative method is proposed to estimate dementia incidence rate before enrollment using prevalent cohort data with left truncation. Furthermore, simulations are used to examine the performance of the estimation of disease incidence under different assumptions of disease incidence rates and excess mortality hazards due to disease. As application, the method is applied to the prevalent cases of dementia from the Honolulu-Asia Aging Study to estimate the dementia incidence rate and to assess the effect of hypertension, Apoe 4 and education on dementia onset.     

Multivariate outlier tests with structured co variance matrices

Outlier tests are developed for multivariate data where there is a structure to the covariance or correlation matrix. Particular structures considered are the block diagonal structure where there are reasons to assume that one set of variables is independent of another, and the equicorrelation structure where it may be assumed that all pairs of variables have the same correlation. Likelihood ratio tests for an outlier are derived for these situations and critical values, under the null hypothesis of no outliers present, are determined for selected sample sizes and dimensions, using Bonferroni bounds or simulation. The powers of the tests are compared with those of the Wilks′ statistic for a variety of situations. It is shown that the test procedures which incorporate knowledge of the correlation structure have considerably greater power than the usual tests particularly in relatively small samples with several dimensions.     

Quadratic subspaces and construction of Bayes invariant quadratic estimators of variance components in mixed linear models

Gnot et al. (J Statist Plann Inference 30(1):223–236, 1992) have presented the formulae for computing Bayes invariant quadratic estimators of variance components in normal mixed linear models of the form where the matrices V _i , 1 ≤ i ≤ k − 1, are symmetric and nonnegative definite and V _k is an identity matrix. These formulae involve a basis of a quadratic subspace containing MV ₁ M,...,MV _k-1 M,M, where M is an orthogonal projector on the null space of X′. In the paper we discuss methods of construction of such a basis. We survey Malley’s algorithms for finding the smallest quadratic subspace including a given set of symmetric matrices of the same order and propose some modifications of these algorithms. We also consider a class of matrices sharing some of the symmetries common to MV ₁ M,...,MV _k-1 M,M. We show that the matrices from this class constitute a quadratic subspace and describe its explicit basis, which can be directly used for computing Bayes invariant quadratic estimators of variance components. This basis can be also used for improving the efficiency of Malley’s algorithms when applied to finding a basis of the smallest quadratic subspace containing the matrices MV ₁ M,...,MV _k-1 M,M. Finally, we present the results of a numerical experiment which confirm the potential usefulness of the proposed methods. Dedicated to the memory of Professor Stanisław Gnot.     

Comparing two independent incidence rates using conditional and unconditional exact tests

Several unconditional exact tests, which are constructed to control the Type I error rate at the nominal level, for comparing two independent Poisson rates are proposed and compared to the conditional exact test using a binomial distribution. The unconditional exact test using binomial p-value, likelihood ratio, or efficient score as the test statistic improves the power in general, and are therefore recommended. Unconditional exact tests using Wald statistics, whether on the original or square-root scale, may be substantially less powerful than the conditional exact test, and is not recommended. An example is provided from a cardiovascular trial.     

灰色组合预测模型及其应用

针对传统回归模型需要的数据量大且建模复杂等缺陷,提出了一种基于灰色关联度和GM(1,1)的灰色组合预测模型;从灰色关联度的视角寻找数据之间的依赖关系,运用GM(1,1)模型预测数据关系的未来发展趋势,进而建立因变量的预测模型;模型体现了回归分析基于事物因果关系的建模思想,同时又具有灰色理论小样本建模的特点;应用该模型对我国2007和2008年度的GDP进行预测,预测结果表明了该模型的有效性及实用性。     

Testing equality of cause-specific hazard rates corresponding to m competing risks among K groups

In this paper, a class of tests is developed for comparing the cause-specific hazard rates of m competing risks simultaneously in K ( 2) groups. The data available for a unit are the failure time of the unit along with the identifier of the risk claiming the failure. In practice, the failure time data are generally right censored. The tests are based on the difference between the weighted averages of the cause-specific hazard rates corresponding to each risk. No assumption regarding the dependence of the competing risks is made. It is shown that the proposed test statistic has asymptotically chi-squared distribution. The proposed test is shown to be optimal for a specific type of local alternatives. The choice of weight function is also discussed. A simulation study is carried out using multivariate Gumbel distribution to compare the optimal weight function with a proposed weight function which is to be used in practice. Also, the proposed test is applied to real data on the termination of an intrauterine device.An erratum to this article can be found at     

Projector operators in the multivariate Zyskind-Martin model

Summary Two quadratic formsS _H andS _E for a testable hypothesis and for an error in the multivariate Zyskind-Martin model with singular covariance matrix are expressed by means of projector operators. Thus the results for the multivariate standard model with identity covariance matrix given by Humak (1977) and Christensen (1987, 1991) are generalized for the case of Zyskind-Martin model. Special cases of our results are formulae forS _H andS _E in Aitken's (1935) model. In the case of general Gauss-Markoff modelS _H andS _E can also be expressed by means of projector operators for some subclasses of testable hypotheses. For these hypotheses, testing in Gauss-Markoff model is equivalent to testing in a Zyskind-Martin model.     

Vec and vech operators for matrices,with some uses in jacobians and multivariate statistics

The vec of a matrix X stacks columns of X one under another in a single column; the vech of a square matrix X does the same thing but starting each column at its diagonal element. The Jacobian of a one-to-one transformation X → Y is then ∣∣?(vecX)/?(vecY) ∣∣ when X and Y each have functionally independent elements; it is ∣∣ ?(vechX)/?(vechY) ∣∣ when X and Y are symmetric; and there is a general form for when X and Y are other patterned matrices. Kronecker product properties of vec(ABC) permit easy evaluation of this determinant in many cases. The vec and vech operators are also very convenient in developing results in multivariate statistics.