对于双未知参数均匀分布的序贯 minimax 估计

统计判决理论的一个重要问题,是对一个给定的分布族,当观测是独立同分布的,作n 次观测的费用为 cn(c>0)时,求其参数的序贯 minimax 估计.关于这一问题,Wald对损失函数 W(θ,d)=(θ-d)~2,得到了从 θ-1/2到 θ+1/2(-∞<θ<∞)上的均匀分布中均值θ的估计.Blyth将 Wald 的结果作了推广和改进.Kiefer 关于损失函数 W(θ,d)=[(θ-d)/θ]~2,解决了从0到 θ(0<θ<∞)上的均匀分布中参数θ的估计问题.本文所要讨论的是含有两个未知参数的均匀分布,其密度为     

竞争风险混合模型的参数估计与检验

本文在独立同分布I型区间删失情形下,研究了竞争风险混合模型中当参数真值是内点时,参数极大似然估计的性质,获得了其强相合性和渐近正态性.在较为宽松的条件下,给出了竞争风险混合模型参数序关系假设检验的检验方法,同时得到了似然比检验统计量及其在零假设下的渐近分布为加权x~2分布,并给出了—个例子并进行了功效比较.     

工具变量线性回归模型的平均估计

针对工具变量线性回归模型的未知参数研究了模型平均框架,该框架能同时适用于独立数据和相依数据.在这一框架下,文章推导了模型平均估计的渐近分布,构造了一个覆盖真实参数的概率趋于预定水平的置信区间,并证明了该置信区间与基于全模型的置信区间渐近等价.最后,文章还进行了模型研究,以考察模型平均估计在有限样本下的表现.     

线性模型中误差方差估计的强相合性的充要条件

本文在只假定误差独立而不必同分布的条件下,得出了基于残差平方和的误差方差估计的强相合性的充要条件。这个条件与试验点列完全无关。这样,就解决了文献[1]中提出的问题。     

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本文讨论了定时截尾样本下三参数Weibull分布修正矩估计(MME)的强相合性.首先证明了修正样本矩的强相合性.然后给出了条件(L),得出结论:若所研究的分布F(x;θ1,θ2,θ3)满足条件(L),修正矩估计θ1,θ2,θ3强相合于参数真值.最后证明了当形状参数δ≥1,即失效率增加时,三参数威布尔分布Wei(x;β,δ,γ)满足条件(L),即MME是强相合的.     

基于局部多项式回归的模型校准抽样估计研究

在抽样估计中,当研究变量与辅助变量之间呈非线性关系时,传统的校准估计方法效果较差,基于非参数回归方法的模型校准估计量则可以很好地解决这一问题。首先,建立描述研究变量和辅助变量之间关系的超总体回归模型,使用非参数中的局部多项式方法得出模型参数的拟合值,并结合校准估计得出局部多项式模型校准估计量,同时给出其方差和方差估计量公式,证明了该估计量具有渐近无偏性、一致性和渐近正态性等优良的统计性质。然后,使用仿真模拟的方法证明在研究变量与研究变量之间呈非线性关系时,该估计量有良好的估计效果。最后,对该估计量在我国政府统计中的应用进行简单的介绍。     

考虑随机投资收益和单边线性索赔的时间依赖更新风险模型的破产概率

本文主要研究一类考虑随机投资收益和相依索赔额的时间依赖的更新风险模型.在该模型中,保险投资收益服从指数Lévy过程,而索赔额服从具有独立同分布步长的单边线性过程.该单边线性过程的步长与索赔到达时间构成独立同分布的随机向量序列,并且该随机向量的分量之间具有运用步长关于索赔到达时间间隔的条件尾概率渐近性刻画的相依关系.当单边线性过程的步长服从重尾分布时,本文得到该更新风险模型破产概率在时间域内的一致渐近估计.     

基于矩和L矩的三参数Ⅰ型广义Logistic分布的参数估计

广义Logistic分布是一族重要的分布,被广泛地应用于生物学、医学、金融管理学,以及气象、水文、地质等领域.迄今为止,对于Logistic分布,统计学者已给出诸多的统计推断理论和方法,以及众多应用成果.令人遗憾的是,对应用非常广泛的广义Logistic分布,特别是具有位置、刻度和形状参数的三参数Ⅰ型广义Logistic分布的研究还有待深入,该分布的应用还需进—步开发和利用.本文利用矩法和L矩法讨论三参数Ⅰ型广义Logistic分布的参数估计,给出两种估计形式下参数的估计方程;证明了在一定的条件下,估计方程的解存在、唯一,且渐近正态地相合于真实参数的结论.通过计算机模拟,比较不同参数、不同样本容量下两种估计的估计效果.     

线性模型的最小二乘估计的中偏差及其重对数律

本文研究了线性模型的最小二乘估计的中偏差.通过估计Laplace渐近积分,得到了随机误差为取值于Rd的相互独立同分布随机变量情形下的中偏差与重对数律的结果.     

相依误差广义线性模型的M估计的Bahadur表示

考虑如下广义线性模型y_i=h(x~T_i,β)+e_i=1,2,…,n,其中e_i=G(…,ε_(i-1),ε_i),h是一个连续可导函数,ε_i是独立同分布的随机变量,并且它的期望为0,方差σ~2有限.本文给出了参数β的M估计,并且得到了该估计的Bahadur表示,该结论推广了线性模型的相关结论.应用M估计的Bahadur表示,得到了相依误差的线性回归模型,poisson模型,logistic模型和独立误差的广义线性模型等模型的渐近性质.     

A systematic approach for examining the impact of calibration uncertainty in disease modeling

In model-based analysis for comparative evaluation of strategies for disease treatment and management, the model of the disease is arguably the most critical element. A fundamental challenge in identifying model parameters arises from the limitations of available data, which challenges the ability to uniquely link model parameters to calibration targets. Consequently, the calibration of disease models leads to the discovery of multiple models that are similarly consistent with available data. This phenomenon is known as calibration uncertainty and its effect is transferred to the results of the analysis. Insufficient examination of the breadth of potential model parameters can create a false sense of confidence in the model recommendation, and ultimately cast doubt on the value of the analysis. This paper introduces a systematic approach to the examination of calibration uncertainty and its impact. We begin with a model of the calibration process as a constrained optimization problem and introduce the notion of plausible models which define the uncertainty region for model parameters. We illustrate the approach using a fictitious disease, and explore various methods for interpreting the outputs obtained.     

混水平列扩充设计的均匀性

在许多工业应用中,通常分步应用跟随设计来考察输入(因子)和产出(响应)间的关系.在许多跟随设计中,在跟随阶段可以加入一些另外的两水平或三水平因子,因为它们在初始阶段可能被忽略但又十分重要.文章在均匀性准则下,提出了中心化L2-偏差意义下的混水平列扩充均匀设计,给出了列扩充设计在中心化L2-偏差下的解析表达式及相应的下界,其可作为搜索均匀设计的基准.进一步,具有一个附加区组因子的列扩充设计是均匀的当且仅当未加区组因子时的列扩充设计是均匀的.     

半参数回归非线性小波误差密度估计

In this paper,a semiparametric regression model in which errors are i.i.d random variables from an unknown density f(·) is considered.Based on Hall et al.(1995),a nonlinear wavelet estimation of f(·) without restrictions of continuity everywhere on f(·) is given,and the convergence rate of the estimators in L2 is obtained.     

Rotator design

The authors study the design of rotators (i.e. networks whose outputs are obtained by a cyclic permutation of their inputs). A direct design can be built with multiplexers. The expansion of rotators (i.e. the building of a large rotator by an interconnection of several smaller rotators) is studied, and three designs are given for it: the common factor, prime factor and near prime factor designs.     

Methods of critical value reduction for type-2 fuzzy variables and their applications

A type-2 fuzzy variable is a map from a fuzzy possibility space to the real number space; it is an appropriate tool for describing type-2 fuzziness. This paper first presents three kinds of critical values (CVs) for a regular fuzzy variable (RFV), and proposes three novel methods of reduction for a type-2 fuzzy variable. Secondly, this paper applies the reduction methods to data envelopment analysis (DEA) models with type-2 fuzzy inputs and outputs, and develops a new class of generalized credibility DEA models. According to the properties of generalized credibility, when the inputs and outputs are mutually independent type-2 triangular fuzzy variables, we can turn the proposed fuzzy DEA model into its equivalent parametric programming problem, in which the parameters can be used to characterize the degree of uncertainty about type-2 fuzziness. For any given parameters, the parametric programming model becomes a linear programming one that can be solved using standard optimization solvers. Finally, one numerical example is provided to illustrate the modeling idea and the efficiency of the proposed DEA model.     

Moment convergence of <Emphasis Type="Italic">Z</Emphasis>-estimators

The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.     

基于Kriging模型和提升小波变换的随机模型修正北大核心CSCD

为提高随机模型修正效率,减小计算量,提出了一种基于Kriging模型和提升小波变换的随机模型修正方法.首先,对加速度频响函数进行提升小波变换,提取第5层近似系数代替原频响函数.其次,采用拉丁超立方抽样抽取待修正样本,将其作为Kriging模型的输入,对应的近似系数作为输出,构建Kriging模型.提出了一种引入莱维飞行(Lévy flight)的蝴蝶优化算法(LBOA),并将其应用于Kriging模型相关参数的寻优中,提高Kriging模型的精度.最后,以最小化Wasserstein距离为目标,通过鲸鱼优化算法求解待修正参数的均值.测试函数结果表明,LBOA在寻优能力、收敛精度和稳定性等方面有了很大的提升.数值算例的修正误差均低于0.4%,验证了所提模型修正方法具有较高的修正精度和效率.     

基于递归型神经网络动力学求解时变凸二次规划

为了在线求解时变凸二次规划问题,实现误差精度更高、求解时间更短和收敛速度更快的目标。本文采用了求解问题更快的时变网络设计参数,选择了有限时间可以收敛的Sign-bi-power激活函数,构造了一种改进的归零神经网络动力学模型。其后,分析了模型的稳定性和收敛性,得到其解能够在有限时间内收敛。最后,在仿真算例中,与传统的梯度神经网络和归零神经网络模型相比,所提模型具有更高的误差精度、更短的求解时间和更快的收敛速度,优于前两种网络模型。     

A New Bound on the Number of Designs with Classical Affine Parameters

The hyperplanes in the affine geometry AG(d, q) yield an affineresolvable design with parameters $2 - (q^d ,q^{d - 1} ,\frac{{q^{d - 1} - 1}}{{q - 1}})$ . Jungnickel [3]proved an exponential lower bound on the number of non-isomorphic affine resolvable designs with these parametersfor d ≥ 3. The bound of Jungnickel was improved recently [5] by a factor of $q^{\frac{{d^2 + d - 6}}{2}} (q - 1)^{d - 2}$ for any d ≥ 4. In this paper, a construction of $2 - (q^d ,q^{d - 1} ,\frac{{q^{d - 1} - 1}}{{q - 1}})$ designs based on group divisible designs is given that yieldsat least $$\frac{{\left( {q^{d - 1} + q^{d - 2} + \cdots + 1} \right)!\left( {q - 1} \right)}}{{\left| {{\text{P}}\Gamma {\text{L(}}d,q{\text{)}}} \right|\left| {{\text{A}}\Gamma {\text{L(}}d,q{\text{)}}} \right|}}$$ non-isomorphic designs for any d ≥ 3. This new bound improves the bound of[5] by a factor of $$\frac{1}{{q^d }}\mathop \Pi \limits_{i = 1}^{(q^{d - 1} - q)/(q - 1)} (q^{d - 1} + i).$$ For any given q and d, It was previously known [2,11] that there are at least 8071non-isomorphic 2-(27,9,4) designs. We show that the number of non-isomorphic 2-(27,9,4) is atleast 245,100,000.     

Interdisciplinary design optimization: A search method

The design of architectural structures frequently involves interdisciplinary aspects and aesthetic considerations which, being of subjective nature, are difficult to quantify. The computer-aided design optimization model presented here, therefore, is an attempt to optimize, in an interdisciplinary context, quantifiable parameters only. The objective function is graphically illustrated to give the designer a means to evaluate the impact of esoteric design decisions on performance variables, such as costs. A search method is used, i.e., evaluation of a discrete number of designs and nonlinear interpolation. The model's system of computer programs is demonstrated on the sample of an anticlastic cable roof structure.This paper contains excerpts from Refs. 1–2.