Book Reviews

Books reviewed:
R.J. Adler, R.E. Feldman & M.S. Taqqu, A Practical Guide to Heavy Tails: Statistical Techniques and Applications.
J.J. Foste, A Beginner's Guide to Data Analysis Using SPSS for Windows.
N. Limnios and G. Oprisan, Semi–Markov Processes and Reliability.     

Confidence Intervals for Current Status Data

Abstract.  The likelihood ratio statistic for testing pointwise hypotheses about the survival time distribution in the current status model can be inverted to yield confidence intervals (CIs). One advantage of this procedure is that CIs can be formed without estimating the unknown parameters that figure in the asymptotic distribution of the maximum likelihood estimator (MLE) of the distribution function. We discuss the likelihood ratio-based CIs for the distribution function and the quantile function and compare these intervals to several different intervals based on the MLE. The quantiles of the limiting distribution of the MLE are estimated using various methods including parametric fitting, kernel smoothing and subsampling techniques. Comparisons are carried out both for simulated data and on a data set involving time to immunization against rubella. The comparisons indicate that the likelihood ratio-based intervals are preferable from several perspectives.     

投资扩张的经济学分析

我国经济运行的态势良好,但存在的问题也不少。其中,投资盲目扩张的冲动较强是个主要矛盾。投资 受预期的影响,非理性预期是投资盲目扩张的一个充分必要条件。将科学发展观引入理性预期的概念之中,能够 提高投资决策和投资行为的科学性。建立健全正式的和非正式的制度安排,发展科学教育事业和提高全民的文化 素质,有利于形成信息的充分性和对称性。     

苍凉的欢愉--评赖少其80岁后的作品

中西文化的碰撞,为20世纪的中国画坛平添了诸多扑朔迷离的景象,也为俯仰于这一背景下的无数个体的艺术生命带来了重重疑惑和困扰.赖少其以其特殊的革命经历、独特的文化积累,在自然生命行将停止运行的关键时期凸显了其艺术生命中最本质、最原始、最朴素、最真挚和最纯净的精神境象,真正实现了中国画由传统向现代的转换过程,从而为20世纪的中国画坛绽放了一枝奇瑰的花朵.     

一类两个相同部件并联的可修系统的稳定性

研究一类两个相同部件并联的可修系统．使用泛函分析方法，特别是Banach空间上的线性算子理论，证明了严格占优本征值的存在性，以及系统解的渐近稳定性，线性稳定性和指数稳定性．     

Expected sample moments of concomitants of selected order statistics

In this paper, the task of determining expected values of sample moments, where the sample members have been selected based on noisy information, is considered. This task is a recurring problem in the theory of evolution strategies. Exact expressions for expected values of sums of products of concomitants of selected order statistics are derived. Then, using Edgeworth and Cornish-Fisher approximations, explicit results that depend on coefficients that can be determined numerically are obtained. While the results are exact only for normal populations, it is shown experimentally that including skewness and kurtosis in the calculations can yield greatly improved results for other distributions.     

Approximation of density functions by orthogonal series with grouped data

Summary Letg(x) andf(x) be continuous density function on (a, b) and let {ϕ_j} be a complete orthonormal sequence of functions onL ₂(g), which is the set of squared integrable functions weighted byg on (a, b). Suppose that over (a, b). Given a grouped sample of sizen fromf(x), the paper investigates the asymptotic properties of the restricted maximum likelihood estimator of density, obtained by setting all but the firstm of the ϑ_j’s equal to0. Practical suggestions are given for performing estimation via the use of Fourier and Legendre polynomial series. Research partially supported by: CNR grant, n. 93. 00837. CT10.     

A Unified Approach to the Approximation of Multivariate Densities

Approximation of a density by another density is considered in the case of different dimensionalities of the distributions. The results have been derived by inverting expansions of characteristic functions with the help of matrix techniques. The approximations obtained are all functions of cumulant differences and derivatives of the approximating density. The multivariate Edgeworth expansion follows from the results as a special case. Furthermore, the density functions of the trace and eigenvalues of the sample covariance matrix are approximated by the multivariate normal density and a numerical example is given     

Estimation for Continuous Branching Processes

The maximum-likelihood estimator for the curved exponential family given by continuous branching processes with immigration is investigated. These processes originated from population biology but also model the dynamics of interest rates and development of the state of technology in economics. It is proved that in contrast to branching processes with discrete space and/or time the MLE gives a unified approach to the inference. In order to include singular subdomains of the parameter space we modify the MLE slightly. Consistency and asymptotic normality for the MLE are considered. Concerning the asymptotic theory of the experiments, all three properties LAQ, LAN, and LAMN occur for different submodels     

A Class of Efficient Non-parametric K-sample Tests for Multivariate Counting Processes with Frailties

A K -sample testing problem is studied for multivariate counting processes with time-dependent frailty. Asymptotic distributions and efficiency of a class of non-parametric test statistics are established for certain local alternatives. The concept of efficiency is to show that for every non-parametric test in this class, there is a parametric submodel for which the optimal test has the same asymptotic power as the non-parametric one. The theory is applied to analyse a diabetic retinopathy study data set. A simulation study is also presented to illustrate the theory