辅助信息下的逆抽样设计算法

通过将逆抽样设计视为一种特殊的二重抽样,建立了二重抽样和为回归估计的二重抽样的一般形式,得到了逆抽样设计算法下的回归估计.模拟分析的结果表明,以回归估计的形式引入较为合适的辅助信息,能够在估计精度上对逆抽样设计算法做出改进.     

双无回答层抽样的三重抽样比率估计量

无回答在抽样调查中经常出现,无回答层再抽样是解决无回答的常用方法.当辅助变量总体均值未知时,本文讨论了双无回答层抽样的三重抽样方法,给出了三重抽样的分层汉森-赫维茨估计量和比率估计量,以及它们的方差和估计方差.给出满足事前给定总调查费用约束的三重抽样过程的最优设计参数,以及比率估计量的方差估计.给定总调查成本,三重抽样的分层汉森—赫维茨估计量与比率估计量进行模拟比较,演示比率估计量的优良性.     

分层三阶段及以上抽样的自加权抽样设计

大型抽样调查总是采用分层多阶段抽样.分层多阶段抽样若采用自加权的抽样设计,则总体总量的估计量形式简单,易于计算.本文提出了分层三阶段及以上抽样的自加权抽样设计方法.     

单纯随机抽样理论之我见

针对一般经济统计教材中普遍存在的关于单纯随机抽样过程中,不同抽样方法下样本方差的无偏性问题提出自己的见解.认为,抽样理论源于实践,重复抽样时有Nn个样本、不重复抽样时有CnN个样本是实际抽样调查工作中普遍采用的方式、方法,更是单纯随机抽样推断理论的源泉.在此基础上数学界将实际工作中各种可能始点的抽样方法赋予理性思考、研究,获得结论:无限制抽样和简单随机抽样条件下样本方差是总体方差的无偏估计量.     

正交表型均匀LH设计和抽样

本文提出了一种新的设计和抽样方法－正交表型均匀LH设计和抽样,证明了这种抽样空间是OALH抽样空间的优良子集。这种设计和抽样空间中所有样本都与初始设计具有同阶低偏差等一些优良性质。并将它用于数值积分,证明了对有关参数的估计的方差阶低于其他抽样。同时还给出了有关的模拟结果。     

重抽样方法在投资组合理论中的应用与实证分析

在投资组合过程中,由于不了解投资对象的总体分布,可能会过高估计风险回报率.利用重抽样方法可以查看高估程度,采用Shrinkage方法可以改善模型,找到最优的分配权重,帮助投资人确定投资金额分配.基于均值-方差模型与重抽样方法,在不允许卖空的情况下,运用R软件得到了有效的投资组合.     

一种满足有效样本量固定的放回抽样方法

相比不放回抽样,放回抽样的实施比较简单,操作性强,但缺点在于单元可能被重复抽到,抽出的有效样本量小于等于样本量,不是固定的。本文应用逆抽样的原理,设计了一种放回抽样方法,满足有效样本量固定,并且估计量的性质优良。     

住户调查中户内样本抽样方法的比较研究

抽样调查是获取社会经济调查数据的主要手段,其抽样设计一般采用分层多阶段不等概的抽样设计。但是,在抽样设计和实际抽样中,人们往往忽视末端样本个体的抽样,本文主要基于中国家庭动态跟踪调查数据对末端样本的概率抽样方法进行比较研究。     

多目标调查的MPPS平衡抽样方法研究

平衡抽样是广受关注的利用辅助信息改善样本结构的抽样方法.MPPS抽样在多目标调查中采用的与多变量规模成比例的入样概率,可以在平衡抽样中精确满足.基于MPPS抽样和平衡抽样的性质,文章提出多目标调查下的MPPS平衡抽样,该方法主要思想是将多个调查变量的辅助信息在确定入样概率和随机抽样过程中同时使用,提高HT估计量精度.模...     

Stein两阶段抽样问题中第一阶段最优抽样量研究

当精度和可靠度给定时，Stein（1945）提出了两阶段抽样方法，构造了同时满足一定可靠度与精度的区间估计．本文则利用数值计算方法，进一步给出了此两阶段抽样中最优的第一阶段抽样量．     

Variabilities of measured and simulated soil structures

The macro-structure of tilled soil varies significantly between replicate samples collected from the field. This is illustrated with data from a grey swelling clay from Victoria, Australia. Soil structure was quantified statistically from studies of linear transects on sections cut through impregnated blocks of undisturbed soil as described previously.Simulated soil structures were generated using the mean parameters measured from actual soil structures. The simulated and actual soil structures exhibited similar variabilities. Not all of the statistical parameters are independent, and some covariances of these are examined.The variabilities of some derived structural quantities and dissimilarity coefficients between replicate soil structures are also examined as functions of sample size. Minimum sample sizes are set which are necessary to distinguish between soil structure of various degrees of similarity.     

The Nonnegative Zero-Norm Minimization Under Generalized Z-Matrix Measurement

In this paper, we consider the zero-norm minimization problem with linear equation and nonnegativity constraints. By introducing the concept of generalized Z-matrix for a rectangular matrix, we show that this zero-norm minimization with such a kind of measurement matrices and nonnegative observations can be exactly solved via the corresponding p-norm minimization with p in the open interval from zero to one. Moreover, the lower bound of sample number for exact recovery is allowed to be the same as the sparsity of the original image or signal by the underlying zero-norm minimization. A practical application in communications is presented, which satisfies the generalized Z-matrix recovery condition.     

基于l2/lq(q=2/3)最小化模型的块稀疏信号恢复

该文主要研究了块稀疏信号的恢复问题.利用q块限制等距性质(0<q≤1),通过极小化混合l₂/l_q(q=2/3)范数,建立了块稀疏信号恢复的一个充分条件,并且得到了在有噪声情形下信号恢复的误差界.通过数值实验,验证了该模型对于块稀疏信号的恢复有较高的成功率.     

修正HS共轭梯度法在大规模信号重构问题中的应用

本义研究了压缩感知在大规模信号恢复问题中应用的问题.利用修正HS共轭梯度法及光滑化方法,获得了具有较好重构效果的算法.数值实验表明用修正HS共轭梯度法解决大规模信号恢复问题是可行的.     

基于l1-l2范数的块稀疏信号重构

压缩感知(compressed sensing,CS) 是一种全新的信息采集与处理的理论框架,借助信号内在的稀疏性或可压缩性,可以从小规模的线性、非自适应的测量中通过求解非线性优化问题重构原信号.块稀疏信号是一种具有块结构的信号,即信号的非零元是成块出现的.受YIN Peng-hang, LOU Yi-fei, HE Qi等提出的l_1-2范数最小化方法的启发,将基于l₁-l₂范数的稀疏重构算法推广到块稀疏模型,证明了块稀疏模型下l₁-l₂范数的相关性质,建立了基于l₁-l₂范数的块稀疏信号精确重构的充分条件,并通过DCA(difference of convex functions algorithm) 和ADMM(alternating direction method of multipliers)给出了求解块稀疏模型下l₁-l₂范数的迭代方法.数值实验表明,基于l₁-l₂范数的块稀疏重构算法比其他块稀疏重构算法具有更高的重构成功率.     

Sharp adaptation for spherical inverse problems with applications to medical imaging

This paper examines the estimation of an indirect signal embedded in white noise for the spherical case. It is found that the sharp minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus, when the linear operator has polynomial decay, recovery of the signal is polynomial, whereas if the linear operator has exponential decay, recovery of the signal is logarithmic. The constants are determined for these classes as well. Adaptive sharp estimation is also carried out. In the polynomial case a blockwise shrinkage estimator is needed while in the exponential case, a straight projection estimator will suffice. The framework of this paper include applications to medical imaging, in particular, to cone beam image reconstruction and to diffusion magnetic resonance imaging. Discussion of these applications are included.     

Recovery of signals from unordered partial frame coefficients

In this paper, we study the feasibility and stability of recovering signals in finite-dimensional spaces from unordered partial frame coefficients. We prove that with an almost self-located robust frame, any signal except from a Lebesgue measure zero subset can be recovered from its unordered partial frame coefficients. However, the recovery is not necessarily stable with almost self-located robust frames. We propose a new class of frames, namely self-located robust frames, that ensures stable recovery for any input signal with unordered partial frame coefficients. In particular, the recovery is exact whenever the received unordered partial frame coefficients are noise-free. We also present some characterizations and constructions for (almost) self-located robust frames. Based on these characterizations and construction algorithms, we prove that any randomly generated frame is almost surely self-located robust. Moreover, frames generated with cube roots of different prime numbers are also self-located robust.     

Weyl eigenvalue asymptotics and sharp adaptation on vector bundles

This paper examines the estimation of an indirect signal embedded in white noise on vector bundles. It is found that the sharp asymptotic minimax bound is determined by the degree to which the indirect signal is embedded in the linear operator. Thus when the linear operator has polynomial decay, recovery of the signal is polynomial where the exact minimax constant and rate are determined. Adaptive sharp estimation is carried out using a blockwise shrinkage estimator. Application to the spherical deconvolution problem for the polynomially bounded case is made.     

Optimum signal and image recovery by the method of alternating projections in fractional Fourier domains

This paper presents a signal and image recovery scheme by the method of alternating projections onto convex sets in optimum fractional Fourier domains. It is shown that the fractional Fourier domain order with minimum bandwidth is the optimum fractional Fourier domain for the method employing alternating projections in signal recovery problems. Following the estimation of optimum fractional Fourier transform orders, incomplete signal is projected onto different convex sets consecutively to restore the missing part. Using a priori information in optimum fractional Fourier domains, superior results are obtained compared to the conventional Fourier domain restoration. The algorithm is tested on 1-D linear frequency modulated signals, real biological data and 2-D signals presenting chirp-type characteristics. Better results are obtained in the matched fractional Fourier domain, compared to not only the conventional Fourier domain restoration, but also other fractional Fourier domains.     

抽样调查中最佳测量次数的确定

现场抽样调查中，由于测量误差的存在，使得所测变量实测值的方差增大，通过增加每个体的测量次数可以控制测量误差，但这样每个体调查费用增大。本文对测量信度Ｒ，每个体测量次数ｍ与相应所需的样本含量ｎｍ、调查费用Ｔｎ的关系进行了探讨，并介绍了如何根据Ｒ，及每个体测量费用占其总费用构成比Ｃ，确定最佳测量次数ｍ值，以达到最佳控制调查费用的目的，这对我们在大型现场调查中进行经济效益分析具有重大的理论指导意义。