连续型经验过程及其Bootstrap逼近

本文利用样条函数将经验分布函数光滑化,从而得到了连续型经验分布函数,进而引进了连续型经验过程,本文讨论了连续型经验分布函数和连续型经验过程的渐进分布,并且证明了连续型经验过程的Bootstrap逼近成立。     

Bilevel “Defender–Attacker” Model with Multiple Attack Scenarios

We consider a bilevel “defender-attacker” model built on the basis of the Stackelberg game. In this model, given is a set of the objects providing social services for a known set of customers and presenting potential targets for a possible attack. At the first step, the Leader (defender) makes a decision on the protection of some of the objects on the basis of his/her limited resources. Some Follower (attacker), who is also limited in resources, decides then to attack unprotected objects, knowing the decision of the Leader. It is assumed that the Follower can evaluate the importance of each object and makes a rational decision trying to maximize the total importance of the objects attacked. The Leader does not know the attack scenario (the Follower’s priorities for selecting targets for the attack). But, the Leader can consider several possible scenarios that cover the Follower’s plans. The Leader’s problem is then to select the set of objects for protection so that, given the set of possible attack scenarios and assuming the rational behavior of the Follower, to minimize the total costs of protecting the objects and eliminating the consequences of the attack associated with the reassignment of the facilities for customer service. The proposed model may be presented as a bilevelmixed-integer programming problem that includes an upper-level problem (the Leader problem) and a lower-level problem (the Follower problem). The main efforts in this article are aimed at reformulation of the problem as some one-level mathematical programming problems. These formulations are constructed using the properties of the optimal solution of the Follower’s problem, which makes it possible to formulate necessary and sufficient optimality conditions in the form of linear relations.     

线性M-回归的Bootstrap逼近

<正> 在讨论某些估计的误差的统计特性时,Efron在[1]中提出了一种Bootstrap方法.设X_1,…,X_n是F的一组独立同分布样本,F_n是对应的经验分布函数,又设X_1,…,X_m是按F_n的重新抽样.我们所关心的是量R(X_1,…,X_n;F)的统计特性,其中R既     

Chernoff-Savage统计量的Bootstrap逼近

本文将Efron提出的Bootstrap方法应用于具有广泛应用的Chernoff-Savage统计量，讨论了它的Bootstrap分布的渐进性质，证明了该统计量的规则化形式的Bootstrap分布弱收敛干正态分布．     

关于“非截尾型L统计量的Bootstrap逼近”一文的更正

关于“非截尾型Ｌ统计量的Ｂｏｏｔｓｔｒａｐ逼近”一文的更正成平（中国科学院系统科学研究所，北京１０００８０）武汉大学安军同志曾致函本人，他指出我们文章［１］引理３．３证明中的“≤”应是“≥”；因此该引理不成立．然而这是否影响原文定理３．１的结论呢？我...     

On the Time-Dependent Delta-Shock Model Governed by the Generalized PóLya Process

One of the widely discussed in the literature and relevant in practice shock models is the delta-shock model that is described by the constant time of a system’s recovery after a shock. However, in practice, as time progresses and due to deterioration of a system, this recovery time is gradually increasing. This important phenomenon was not discussed in the literature so far. Therefore, in this paper, we are considering a time-dependent delta-shock model, i.e., the recovery time becomes an increasing function of time. Moreover, we assume that shocks occur according to the generalized Pólya process that contains the homogeneous Poisson process, the non-homogeneous Poisson process and the Pólya process as particular cases. For the defined survival model, we derive the corresponding survival function and the mean lifetime and study the related optimal replacement policy along with some relevant stochastic properties.

     

Periodicity in a “Food-limited” Population Model with Toxicants and Time Delays

Abstract With the help of a continuation theorem based on Gaines and Mawhin's coincidence degree,westudy the global existence of positive periodic solutions of a "food-limited" population model with toxicants andtime delays.Some new results are obtained.     

L-统计量的Bootstrap逼近速度

在较为理想的条件下,本文获得了L-统计量的Bootstrap逼近速度.同时作为补充命题,我们给出了一个L-统计量方差估计的几乎处处收敛性。     

密度泛函核估计的Bootstrap逼近

设Ｘ１，．．．，Ｘｎ是从分布密度函数为ｆ的总中抽取的ｉｉｄ样本，μ＝ＥＸ１本文研究了密度泛函θ＝ｆ（μ）的核型估计，ｆｎ（ｘ）为通常的Ｒｏｓｅｎｂｌａｔｔ－Ｐａｒｚｅｎ核估计。     

两个回归函数相等的Bootstrap检验

两个回归参数相等性检验一直是统计界感兴趣的问题之一．在这篇文章中，四个检验统计量被用于度量两曲线的差异，在原假设下统计量的分布采用向量数据的重复抽样来逼近，并给出了—些模拟结果．     

On best approximations by analogs of “proper” and “improper” hyperbolic crosses

The exact approximation orders for the classes H _q ^Ω are calculated for the case in which Ω(t) contains both power and logarithmic multipliers. For these classes, the exact orders of best approximation by analogs of “improper” hyperbolic crosses are also obtained.     

Extraction of subsystems “Majorized” by the rademacher system

In this paper it is proved that from any uniformly bounded orthonormal system {f _n} _n=1 ^∞ of random variables defined on the probability space (Ω, ε, P), one can extract a subsystem {fni} _i ^{Emphasis>=1/∞} majorized in distribution by the Rademacher system on [0, 1]. This means that {

独立非同分布情况的光滑Bootstrap逼近

Bootstrap方法一般只适于iid情况,当抽样X_1,…,X_n为独立但不是同分布情况时,本文采用光滑Bootstrap方法,并证明了对于均值这种逼近与iid时Bootstrap逼近具有同样理想的结果。     

线性模型误差方差估计的Bootstrap逼近

<正> §1.引言 1979年,Efron为估计基于独立观测值的统计量的分布,提出了一种很一般的重新抽样程序,称为Bootstrap:以一样本情形为例,设从分布F完全未知的总体中抽得大小为n的简单随机样本X_i=x_i,i=1,…,n.记X=(X_1,…,X_n),x=(x_1,…,x_n),它们分别表示随机样本及其特定的观测值.今给定一个随机变量R(X,F),它可能不仅依赖于X而且依赖于未知分布F.问题是要根据观测数据x去估计R的抽样分布。     

对Bootstrap方法的自助抽样的改进

Bootstrap方法是一种常用的统计推断方法,它的无先验性,以及计算过程中只需要实际的观测数据,使得其可方便的应用于实际的数据处理之中。对连续情形而言,Bootstrap本身的计算特性限制了自助样本的生成范围,即只能从原样本再采样,从而使得自助分布产生偏离,无法渐近于真实情形。鉴于此不足,本文提出了改进的Bootstrap方法,它通过对自助样本生成范围的拓展,克服了这一不足,获得了更加精确的参数估计。     

条件中位数的核估计及其Bootstrap逼近

本文讨论了固定样本时条件中位数的核估计及其Bootstrap逼近的有关性质,即证明了核估计的a·s渐近正态性和它的Bootstrap统计量方差的强相合性。     

回归系数最小二乘估计的Bootstrap估计

本文对线性模型的回归系数β的线性函数α＾Ｔβ的最小二乘估计α＾Ｔβ建立了一种新的ｂｏｏｔｓｔｒａｐ逼近，给出了逼近的相合性定量，得到了ｏ（ｎ＾－１／２）的逼近速度。     

About the Power Law of the PageRank Vector Component Distribution. Part 2. The Buckley–Osthus Model,Verification of the Power Law for This Model,and Setup of Real Search Engines

This paper continues article [13]. Here we consider the Buckley–Osthus model for formation of an Internet network. We numerically calculate the PageRank vector for networks generated by this model.We show that the components of this vector are distributed according to a power law. We also discuss the computational aspects of this model with respect to the numerical methods for calculation of the PageRank vector, which were presented in the first part of the work. Finally, we describe a more general model for web-page ranking and some approaches to solve the optimization problem arising in this model learning.