Simple-Tree Weighted Logrank Tests for Right-Censored Data

In this paper we are concerned with the problem of testing against the simple-tree alternative that there is at least one treatment more effective than the control when data are subject to random right-censorship. A class of tests based on linear combinations of two-sample weighted logrank statistics each comparing an individual treatment with the control is proposed. Asymptotic relative efficiencies of the simple-tree versions of Gehan-Wilcoxon, logrank and Peto-Prentice-Wilcoxon under Lehmann and scale alternatives are evaluated for various combinations of survival distributions and censoring probabilities. The results of a Monte Carlo level and power study are presented. An illustrated numerical example is also reported.     

A nonparametric test for a two-sample scale problem based on subsample medians

A nonparametric test for the two-sample scale problem is proposed by considering the subsample medians of three observations. The proposed statistic has the advantage of not requiring the two distribution functions to have a common median, but rather requiring them to have any common quantile of order α,0≤α≤1 (not necessarily 1/2), which is assumed to be known. Pitman efficiency considerations indicate that the proposed test performs well relative to tests already existing in the literature for heavy tailed distributions.     

一个有效估计:半参数非时齐扩散模型的局部线性复合分位回归估计

主要研究半参数非时齐扩散模型的参数估计问题.基于非时齐扩散模型的离散观测样本,首先得到漂移参数的局部线性复合分位回归估计,并证明估计量的渐近偏差、渐近方差和渐近正态性.其次,讨论了带宽的选择和局部线性复合分位回归估计关于局部线性最小二乘估计的渐近相对效,所得到的局部估计较局部线性最小二乘估计更为有效.最后,通过模拟说明了局部线性复合分位回归估计比局部线性最小二乘估计的模拟效果更好.     

Multivariate Percentile Tests for Incomplete Data

In this paper, we consider the percentile test procedures for multivariate and right censored data. Because of the involvement of censoring distribution into the distribution of the proposed test statistic, we study the asymptotic normality using the estimated covariance matrix. Finally, we derive the asymptotic relative efficiency and illustrate our procedures with an example.     

The influence function of the Stahel–Donoho estimator of multivariate location and scatter

This article derives the influence function of the Stahel–Donoho estimator of multivariate location and scatter for elliptical distributions. Local robustness and asymptotic relative efficiency are studied. The expressions obtained for the influence functions coincide with those of one-step reweighted estimators.     

On the Ranked-Set Sampling M-Estimates for Symmetric Location Families

The ranked-set sampling (RSS) is applicable in practical problems where the variable of interest for an observed item is costly or time-consuming but the ranking of a set of items according to the variable can be easily done without actual measurement. In this article, the M-estimates of location parameters using RSS data are studied. We deal mainly with symmetric location families. The asymptotic properties of M-estimates based on ranked-set samples are established. The properties of unbalanced ranked-set sample M-estimates are employed to develop the methodology for determining optimal ranked-set sampling schemes. The asymptotic relative efficiencies of ranked-set sample M-estimates are investigated. Some simulation studies are reported.     

Weighted Kaplan-Meier Tests for Umbrella Alternatives

The problem of testing for umbrella alternatives in a one-way layout with right-censored survival data is considered. Testing procedures based on the two-sample weighted Kaplan-Meier statistics suggested by Pepe and Fleming (1989, Biometrics, 45, 497–507; 1991, J. Roy. Statist. Soc. Ser. B, 53, 341–352) are suggested for both cases when the peak of the umbrella is known or unknown. The asymptotic relative efficiency of the weighted Kaplan-Meier test and the weighted logrank test proposed by Chen and Wolfe (2000, Statist. Sinica, 10, 595–612) is computed for the umbrella peak-known setting where the piecewise exponential survival distributions have the proportional or crossing hazards, or the related hazards differ at early or late times. Moreover, the results of a Monte Carlo study are presented to investigate the level and power performances of the umbrella tests. Finally, application of the proposed procedures to an appropriated data set is illustrated.     

Approximate energy minimization for large Lennard-Jones clusters

We have designed a simple method to place particles on lattices, concentric shells and icosahedral concentric layers for minimizing the total energy of Lennard-Jones clusters, approximately, by analytical means. The most significant difference of our schemes from others is the dramatic reduction of parameters, which allows the study of large clusters, not possible otherwise. We present the derivation of formulae for minimal per-particle energy and for inter-particle distance. We also present their asymptotic values for large number of particles.     

A computational methodology to study coupled physical processes over partitioned domains

In this paper, we describe a computational methodology to couple physical processes defined over independent subdomains, that are partitions of a global domain in three-dimensions. The methodology presented helps to compute the numerical solution on the global domain by appropriately piecing the local solutions from each subdomain. We discuss the mixed method formulation for the technique applied to a model problem and derive an error estimate for the finite element solution. We demonstrate through numerical experiments that the method is robust and reliable in higher dimensions.     

Iterative algorithms for large partitioned linear systems,with applications to image reconstruction

We present a unifying framework for a wide class of iterative methods in numerical linear algebra. In particular, the class of algorithms contains Kaczmarz's and Richardson's methods for the regularized weighted least squares problem with weighted norm. The convergence theory for this class of algorithms yields as corollaries the usual convergence conditions for Kaczmarz's and Richardson's methods. The algorithms in the class may be characterized as being group-iterative, and incorporate relaxation matrices, as opposed to a single relaxation parameter. We show that some well-known iterative methods of image reconstruction fall into the class of algorithms under consideration, and are thus covered by the convergence theory. We also describe a novel application to truly three-dimensional image reconstruction.     

Likelihood-based imputation inference for mean functionals in the presence of missing responses

This paper considers a semiparametric model which parameterizes only the conditional density of a response given covariates and allows the marginal distribution of the covariates to be completely arbitrary when responses are missing. Different estimators with asymptotic normality for the mean of the response variable are derived, respectively, in the two cases where auxiliary information is available or not. The resulting asymptotic behaviors show that the use of auxiliary information improves inference via empirical likelihood approach. This research was supported by National Natural Science Foundation of China (Key grant 10231030, Special grant 10241001).     

The existence of large set of symmetric partitioned incomplete latin squares

In this paper, we investigate the existence of large sets of symmetric partitioned incomplete latin squares of type g^u (LSSPILSs) which can be viewed as a generalization of the well‐known golf designs. Constructions for LSSPILSs are presented from some other large sets, such as golf designs, large sets of group divisible designs, and large sets of Room frames. We prove that there exists an LSSPILS(g^u) if and only if u ≥ 3, g(u ? 1) ≡ 0 (mod 2), and (g, u) ≠ (1, 5).     

Ramsey functions involving with large

For fixed integers m,k2, it is shown that the k-color Ramsey number r_k(K_m,n) and the bipartite Ramsey number b_k(m,n) are both asymptotically equal to k^mn as n→∞, and that for any graph H on m vertices, the two-color Ramsey number is at most (1+o(1))n^m+1/(logn)^m-1. Moreover, the order of magnitude of is proved to be n^m+1/(logn)^m if H≠K_m as n→∞.     

Fitting and validation of a bivariate model for large claims

We consider an extended version of a model proposed by Ledford and Tawn [Ledford, A.W., Tawn, J.A., 1997. Modelling dependence within joint tail regions. J. R. Stat. Soc. 59 (2), 475-499] for the joint tail distribution of a bivariate random vector, which essentially assumes an asymptotic power scaling law for the probability that both the components of the vector are jointly large. After discussing how to fit the model, we devise a graphical tool that analyzes the differences between certain empirical probabilities and model based estimates of the same probabilities. The asymptotic normality of these differences allows the construction of statistical tests for the model assumption. The results are applied to claims of a Danish fire insurance and to medical claims from US health insurances.     

Spaces with large relative extent

In this paper, we prove the following statements: (1) For every regular uncountable cardinal κ, there exist a Tychonoff space X and Y a subspace of X such that Y is both relatively absolute star-Lindelöf and relative property (a) in X and e(Y, X) ? κ, but Y is not strongly relative star-Lindelöf in X and X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly relative star-Lindelöf in X (hence, relative star-Lindelöf), but Y is not absolutely relative star-Lindelöf in X.     

Strong asymptotics for Sobolev orthogonal polynomials in the complex plane

We obtain the strong asymptotics for the sequence of monic polynomials minimizing the norm

     

Gaps in samples of geometric random variables

In this note we continue the study of gaps in samples of geometric random variables originated in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239] and continued in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be/di/mcs/louchard/〉 (number 81 on the list) or at 〈http://math.sun.ac.za/∼ prodinger/pdffiles/gapsAPRIL27.pdf.〉] In particular, since the notion of a gap differs in these two papers, we derive some of the results obtained in Louchard and Prodinger [The number of gaps in sequences of geometrically distributed random variables, Preprint available at 〈http://www.ulb.ac.be/di/mcs/louchard/〉 (number 81 on the list) or at 〈http://math.sun.ac.za/∼prodinger/pdffiles/gapsAPRIL27.pdf.〉] for gaps as defined in Hitczenko and Knopfmacher [Gap-free compositions and gap-free samples of geometric random variables. Discrete Math. 294 (2005) 225-239].     

Interval DEA模型中决策单元的投影问题

在传统的DEA模型中,最优相对效率模型是在不大于1的范围内研究决策单元的效率的,最差相对效率模型是在不小于1的范围内研究决策单元的效率,这两种模型在研究投影问题时,是在不同的范围内进行的,有一定的片面性.将在interval DEA模型中,研究决策单元的投影问题,该模型是在相同的约束域内研究最优和最差相对效率模型,得出的结论将更加全面,通过两个定理给出了非DEA有效的决策单元在DEA有效面上的投影表达式和非DEA无效的决策单元在DEA无效面上的投影表达式.同时,通过一个实例对决策单元在interval DEA模型中的投影结果与在传统的DEA模型的投影结果进行了比较,发现投影结果比传统模型得到的投影结果对实际的生产有更强的指导意义.