PPS整群抽样下的比估计量

本文研究有辅助指标的ＰＰＳ整群抽样,构造了总体均值和总值的ＰＰＳ比估计量,证明ＰＰＳ比估计量是可用的,给出ＰＰＳ比估计量优于ＰＰＳ估计量的条件并讨论其优良性．     

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.     

排序下PPS抽样估计量的修正与应用

受许多事物具有齐夫现象的启发,本文提出了排序后PPS抽样方法,并给出了修正汉森-赫维茨估计量及其方差。在此过程中本文解决了,长期以来抽样调查实践中将重要单元直接入样时,多少重要单元直接入样没有明确方法的问题,本文给出了理论依据和具体的确定方法。最后通过一个例子和中国城市人口抽样调查的案例,展示了修正汉森-赫维茨估计量的优势,并对这一研究方法做了总结和展望。     

基于二相抽样的PPS二阶抽样

研究初级单元大小未知时基于二相抽样的PPS二阶抽样，给出总体总值的估计量，估计量的方差及方差的估计量。     

为PPS抽样而进行双重抽样的方法

本文把双重抽样技术用于ＰＰＳ抽样，给出了该方法下总体总值的无偏估计量，估计量的方差及方差的无偏估计公式。     

可加模型的两阶段局部M-估计

研究了可加模型分量回归函数的局部M-估计, 针对分量回归函数及其导数提出了两阶段局部M-估计的方法. 在较广泛的条件下建立了估计量的渐近正态性理论, 估计量具有先知性质(oracle property), 即在估计某一分量回归函数时,其他分量回归函数是否已知不影响估计量的渐近性质. 渐近理论包括了两类常用的估计量,即最小二乘估计和最小一乘估计. 当ψ是连续的且是非线性时,估计量的实施非常耗时,为了减轻计算的负担, 提出了一步局部M-估计量, 并证明了在初始估计量足够好的情形下, 一步局部M-估计量与完全迭代所得到的估计量具有相同的渐近估计效率, 这使得两阶段局部M-估计的方法较为实用. 两阶段局部M-估计量继承了局部多项式估计的优点, 同时克服了其在最小二乘准则下不稳健的缺点. 另外, 还讨论了估计方法实施方面的细节及有关参数的选择方法. 数值模拟结果及实际例子说明了两阶段局部M-估计方法的优点及实用性.     

PPS适应性整群抽样下估计量的研究

在群规模存在差异时,最有效的抽样方法是PPS整群抽样;在单元存在聚集性且总体信息不明确时,使用PPS适应性整群抽样是最有效的.利用PPS适应性整群抽样设计中的样本外推机制产生的样本信息,对HH和HT估计进行调整,提出修正的HH和HT估计,并对估计量的性质进行了研究.     

基于分层抽样的校准方法分别比率-乘积估计研究

比率估计在抽样估计阶段利用辅助信息,提高了估计量的估计精度,是抽样调查中一类较为常用的估计方法,但现有的一些比率估计方法均具有各自的最优条件,这在一定程度上影响了它们在实际调查中的应用。为了解决比率估计的最优限制问题,本文引入了校准估计方法,并基于分层抽样研究了总体均值的校准方法分别比率-乘积估计量。在大样本情况下,本文推导了新估计量的估计偏差和均方误差,说明新估计量具有渐近无偏性,并在估计量均方误差最小时,得到了总体参数的渐近最优估计量和渐近最优估计量的方差。在模拟研究中,根据比率估计量的最优条件是否满足,本文生成了两种不同的总体,对比分析了新估计量和现有比率估计量的估计效果,结果表明在两种不同的情况下,新估计量的估计效果均优于现有估计量的估计效果。最后,本文利用一个实际例子,验证了新估计量的有效性和实用性。     

二阶抽样总体比率的估计

本文研究二阶抽样下总体比率的估计问题, 就若干种情形给出总体比率的几种可行的估计量,讨论了它们的统计性质.     

存在随机解释变量的平行数据模型的处理

本文研究了平行数据模型中存在随机解释变量的解决方法:构造了模型设定的假设检验,给出了参数的一致估计量,并通过建立山东省城镇家庭烟草消费额模型进行了实证分析.     

PPS抽样回归估计量及其在两相抽样中的应用

本文针对交通运输量抽样调查中存在的波动系数问题，讨论在ＰＰＳ的抽样条件下，回归估计量的构造及其在两相抽样中的应用     

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。     

Stratification and sample size of data sources for agricultural mathematical programming models

A comparison is made between the variance of the estimator of the total of a variable obtained from both a simple and a stratified random sampling, in which the sample sizes of some strata are equal to the stratum population size.It is shown that in this case, the advantage of the stratified sample could depend on the sample size. The paper presents inequalities that determine, as a function of the sample size, when the variance of the estimator obtained with simple sampling is lower than the variance obtained with the stratified sampling. The results give insight in order to prevent overstratification.     

右删失长度偏差数据分位数差的非参数估计

利用长度偏差数据所特有的辅助信息,对带右删失的长度偏差数据的分位数差提出了一种新的非参数估计.该方法提高了估计的有效性,所得的估计量形式简洁,便于计算.同时,本文用经验过程理论建立了该分位数差估计的相合性及渐近正态性,并给出方差估计的重抽样方法.本文还通过数值模拟考察了该估计量在有限样本下的表现,并将其应用到一个关于老年痴呆的实际数据中.     

基于平衡样本的校准估计研究--以规模以下工业企业测算为例

为解决规模以下工业企业调查中存在的样本代表性不足的问题,提出基于平衡样本的校准估计方法,并得出相应的估计量和估计量方差。该方法在抽样设计阶段采用了平衡抽样设计,在估计阶段采用了校准估计方法,较大限度地使用了辅助信息;通过数据分析得出基于平衡样本的校准估计方法要优于基于平衡抽样的HT估计方法。同时,为满足平衡变量间线性无关的假定,提出使用主成分分析、切片逆回归和切片平均方差估计三种方法对相关的平衡变量进行处理的思路。该方法对我国规模以下工业企业调查的完善具有理论与实践的双重意义,可适当的推广至我国政府统计的其他调查中。     

On the Bias of the Generalized Regression Estimator in Survey Sampling

It is well known that the generalized regression (GREG) estimator of the finite population total is asymptotically unbiased. Consequently, bias is negligible when the sample size is large. But the magnitude of the bias is not known, if we are estimating small areas or operating with small samples. Furthermore, beside the sample size, the bias depends on the auxiliary variables, on their relation to the study variable and on the sampling design. In small samples it is important to know sources of the bias and in some cases to use a bias-corrected regression estimator. The aim of the present paper is to derive approximate bias expressions of the GREG estimator under different population models and different sampling designs to study the magnitude of the bias.      

An innovative Bayesian sequential censored sampling inspection method and application to test design

This paper proposes an innovative Bayesian sequential censored sampling inspection method to improve the inspection level and reduce the sample size in acceptance test plans for continuous lots. A mathematical model of Bayesian sequential censored sampling is built, where a new inspection parameter is created and two types of risk are modified. As the core of Bayesian risk formulas, a new structure method of the prior distribution is presented by combining the empirical distribution with the uncertainty of the estimation. To improve the fitting accuracy of parameter estimation, an adaptive genetic algorithm is applied and compared with different parameter estimation methods. In the prior distribution, a prior estimator is introduced to design a sampling plan for continuous lots. Then, three types of producer's and consumer's risks are derived and compared. The simulation results indicate that the modified Bayesian sampling method performs well, with the lowest risks and the smallest sample size. Finally, a new sequential censored sampling plan for continuous lots is designed for the accuracy acceptance test of an aircraft. The test results show that compared with the traditional single sampling plan, the sample size is reduced by 66.7%, saving a vast amount of test costs.     

Bounds on entanglement dimensions and quantum graph parameters via noncommutative polynomial optimization

This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery using a random subset of entries observed with additive noise under general non-uniform and unknown sampling distributions. This method significantly relaxes the uniform sampling assumption imposed for the widely used nuclear-norm penalized approach, and makes low-rank matrix recovery feasible in more practical settings. Theoretically, we prove that the proposed estimator achieves fast rates of convergence under different settings. Computationally, we propose an alternating direction method of multipliers algorithm to efficiently compute the estimator, which bridges a gap between theory and practice of machine learning methods with max-norm regularization. Further, we provide thorough numerical studies to evaluate the proposed method using both simulated and real datasets.