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     

Efficient Estimation of a Distribution Function under Quadrant Dependence

LetX₁,X₂, ..., be real-valued random variables forming a strictly stationary sequence, and satisfying the basic requirement of being either pairwise positively quadrant dependent or pairwise negatively quadrant dependent. LetF^ be the marginal distribution function of theX_ips, which is estimated by the empirical distribution functionF_n and also by a smooth kernel-type estimateF_n, by means of the segmentX₁, ...,X_n. These estimates are compared on the basis of their mean squared errors (MSE). The main results of this paper are the following. Under certain regularity conditions, the optimal bandwidth (in the MSE sense) is determined, and is found to be the same as that in the independent identically distributed case. It is also shown thatn MSE(F_n(t)) andnMSE (F^_n(t)) tend to the same constant, asn→∞ so that one can not discriminate be tween the two estimates on the basis of the MSE. Next, ifi(n) = min {k∈{1, 2, ...}; MSE (F_k(t)) ≤ MSE (F_n(t))}, then it is proved thati(n)/n tends to 1, asn→∞. Thus, once again, one can not choose one estimate over the other in terms of their asymptotic relative efficiency. If, however, the squared bias ofF^_n(t) tends to 0 sufficiently fast, or equivalently, the bandwidthh_n satisfies the requirement thatnh³_n→ 0, asn→∞, it is shown that, for a suitable choice of the kernel, (i(n) ?n)/(nh_n) tends to a positive number, asn→∞ It follows that the deficiency ofF_n(t) with respect toF^_n(t),i(n) ?n, is substantial, and, actually, tends to ∞, asn→∞. In terms of deficiency, the smooth estimateF^_n(t) is preferable to the empirical distribution functionF_n(t)     

具有三次代数曲线解的五次系统的极限环

本文利用Maple软件强大的符号计算能力,得到了以 y=ax~3+bx~2+cx+d 为解的平面五次多项式系统的特征,由此证明了该系统在奇点的邻域内可以存在极限环。     

大耦合孔对速调管谐振腔参数的影响

论述大耦合孔对相对论速调管谐振腔的电场分布和特性参数（包括谐振频率、品质因数、特性阻抗、耦合系数等）影响的简要的理论分析与实验研究,以及相应参数的测试方法,并提出了新的耦合孔结构,解决了大耦合孔对谐振腔谐振频率、耦合系数、径向、圆周方向的电场分布的不良影响,其结果对高功率微波器的设计有重要的参考价值。     

理清大经贸战略思路牵引重庆经济快速发展

针对重庆直辖市的特殊市情,提出《重庆市未来五年到2010年对外经贸发展规划》的修改意见:规划的着力点、重庆外经贸特征与自身条件、定位、争取优惠条件、利用外资、货物贸易、服务贸易、经营管理体制改革、基础建设等。     

深化教学改革 搞好课程建设——《硅热工》课程建设初探

从优化课程体系、教材建设、强化实践环节、改进教学方法和手段、加强师资队伍建设等方面对《硅热工》课程的教学进行改革,提出了具体的措施和意见.     

减少流液洞中玻璃液回流

分析了流液洞中玻璃液流情况,提出了流液洞设计和使用中消除或减少回流的措施。     

宏观连续交通流数值模拟

应用交通流宏观连续模型,模拟上下游信号灯作异步周期变化的协调信号灯路段的交通流动,经数值计算比较,选择改进Ｍｕｒｍａｎ格式求解．结果表明：改进Ｍｕｒｍａｎ格式能准确捕捉交通流中无振荡“激波”位置．