序贯调整估计量——不完全事后分层估计的新方法

在使用多个分类变量对样本进行交叉事后分层时,边缘总值已知、格子总值未知的不完全事后分层问题是估计时经常面临的情况。序贯调整估计量是本论文提出的解决这一问题的新方法。在详细介绍了序贯调整估计程序后,论文用随机模拟的方法研究了该估计量的数学性质,并将其与经典的不完全事后分层估计量做了比较。     

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.     

人口总数估计:基于三系统估计量与比率估计量的组合方法

受多种因素影响,人口普查结果不可避免地偏离真实人口总数,如何构造一个统计性质优良,适用范围广的人口总数估计量,精准把握人口变动趋势是政府统计工作的重要议题.本文解读了英国统计局普查年人口总数估计的经验方法,据此提出三系统估计量与比率估计量组合的人口总数估计方法.模拟研究结果表明,在人口总体合理分层的基础上,新方法能较好...     

在几种常见的抽样方案下的事后分层

本文给出系统抽样，放回不等概率抽样及二阶不等概率抽样情况下总体均值的事后分层估计，估计量的方差和它的无偏估计。     

多阶等距抽样下总体总值估计量的方差估计

本文给出了多阶抽样下构造总体总值估计量的方差估计量的一种方法．由此，可以得到多阶等距抽样下总体总值估计量的方差估计．     

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.     

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。     

美国2000年和2010年人口普查质量评估方法解读

人口普查后独立组织一次调查估计其覆盖误差率。美国从1980年开始在人口普查的事后质量检查中使用双系统估计量来估计人口总体真实人口数,并依据它来估计普查的覆盖误差率。后来,这种估计量在世界上其他一些国家人口普查的事后质量检查中也先后被采用。本文以美国2000年人口普查的事后质量检查方案ACE和2010年将要实施的新方案CCM为基础,解读构造双系统估计量的若干理论与实践问题。     

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。     

基于双系统估计量的中国非普查年人口总数估计

针对当前中国非普查年人口总数估计方法的不足,本文提出利用人口抽样调查及其事后质量评估调查数据,构造基于捕获再捕获模型的非普查年人口总数双系统估计量。首先,介绍双系统估计量的构造及其估计方法。其次,研究如何利用刀切法构建双系统估计量的方差估计。最后,通过一组模拟数据演示非普查年人口总数双系统估计量及其方差估计的构造过程。本文的研究能显著提高中国非普查年人口总数估计的准确性和可靠性,并对未来中国人口抽样调查的方案设计提供理论指导。     

Efficient Non-Iterative and Nonparametric Estimation of Heterogeneity Variance for the Standardized Mortality Ratio

In this paper the situation of extra population heterogeneity in the standardized mortality ratio is discussed from the point-of-view of an analysis of variance. First, some simple non-iterative ways are provided to estimate the variance of the heterogeneity distribution without estimating the heterogeneity distribution itself. Next, a wider class of linear unbiased estimators is introduced and their properties investigated. Consistency is shown for a wide sub-class of estimators charactererized by the fact that the associated linear weights are within some positive, finite bounds. Furthermore, it is shown that an efficient estimator is often provided when the weights are proportional to the expected counts.     

Bias expansion of spatial statistics and approximation of differenced lattice point counts

Investigations of spatial statistics, computed from lattice data in the plane, can lead to a special lattice point counting problem. The statistical goal is to expand the asymptotic expectation or large-sample bias of certain spatial covariance estimators, where this bias typically depends on the shape of a spatial sampling region. In particular, such bias expansions often require approximating a difference between two lattice point counts, where the counts correspond to a set of increasing domain (i.e., the sampling region) and an intersection of this set with a vector translate of itself. Non-trivially, the approximation error needs to be of smaller order than the spatial region’s perimeter length. For all convex regions in 2-dimensional Euclidean space and certain unions of convex sets, we show that a difference in areas can approximate a difference in lattice point counts to this required accuracy, even though area can poorly measure the lattice point count of any single set involved in the difference. When investigating large-sample properties of spatial estimators, this approximation result facilitates direct calculation of limiting bias, because, unlike counts, differences in areas are often tractable to compute even with non-rectangular regions. We illustrate the counting approximations with two statistical examples.     

Sieve maximum likelihood estimation for doubly semiparametric zero-inflated Poisson models

For nonnegative measurements such as income or sick days, zero counts often have special status. Furthermore, the incidence of zero counts is often greater than expected for the Poisson model. This article considers a doubly semiparametric zero-inflated Poisson model to fit data of this type, which assumes two partially linear link functions in both the mean of the Poisson component and the probability of zero. We study a sieve maximum likelihood estimator for both the regression parameters and the nonparametric functions. We show, under routine conditions, that the estimators are strongly consistent. Moreover, the parameter estimators are asymptotically normal and first order efficient, while the nonparametric components achieve the optimal convergence rates. Simulation studies suggest that the extra flexibility inherent from the doubly semiparametric model is gained with little loss in statistical efficiency. We also illustrate our approach with a dataset from a public health study.     

The proportional hazards model for multiple type recurrent gap times

Recurrent events data and gap times between recurrent events are frequently encountered in many clinical and observational studies, and often more than one type of recurrent events is of interest. In this paper, we consider a proportional hazards model for multiple type recurrent gap times data to assess the effect of covariates on the censored event processes of interest. An estimating equation approach is used to obtain the estimators of regression coefficients and baseline cumulative hazard functions. We examine asymptotic properties of the proposed estimators. Finite sample properties of these estimators are demonstrated by simulations.     

On a class of almost unbiased ratio estimators

Summary Murthy and Nanjamma [4] studied the problem of construction of almost unbiased ratio estimators for any sampling design using the technique of interpenetrating subsamples. Subsequently, Rao [7], [8] has given a general method of constructing unbiased ratio estimators by considering linear combinations of the two simple estimators based on the ratio of means and the mean of ratios. However, it is difficult to choose an optimum weight (Rao [9]) which minimizes the variance of the combined estimator since the weights are random in certain cases. In this note, we consider a different method of combining these estimators and obtain a general class of almost unbiased ratio estimators of which Murthy and Nanjamma's is a particular case and derive an optimum in this class. The case of simple random sampling where a similar class of almost unbiased ratio estimators can be developed is briefly discussed. The results are illustrated by means of simple numerical examples.     

On exponential rates of likelihood ratio estimators for location parameters

In this paper the exponential rates, bounds, and local exponential rates for likelihood ratio estimators are studied. Under certain regularity conditions, a family of likelihood ratio estimators is shown to be admissible in exponential rate. It is also shown that the maximum likelihood estimator is the limit of this family of estimators.     

Mixtures of semiparametric varying coefficient models for longitudinal data with nonignorable dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.     

Bivariate Birnbaum–Saunders distribution and associated inference

Univariate Birnbaum–Saunders distribution has been used quite effectively to model positively skewed data, especially lifetime data and crack growth data. In this paper, we introduce bivariate Birnbaum–Saunders distribution which is an absolutely continuous distribution whose marginals are univariate Birnbaum–Saunders distributions. Different properties of this bivariate Birnbaum–Saunders distribution are then discussed. This new family has five unknown parameters and it is shown that the maximum likelihood estimators can be obtained by solving two non-linear equations. We also propose simple modified moment estimators for the unknown parameters which are explicit and can therefore be used effectively as an initial guess for the computation of the maximum likelihood estimators. We then present the asymptotic distributions of the maximum likelihood estimators and use them to construct confidence intervals for the parameters. We also discuss likelihood ratio tests for some hypotheses of interest. Monte Carlo simulations are then carried out to examine the performance of the proposed estimators. Finally, a numerical data analysis is performed in order to illustrate all the methods of inference discussed here.     

Asymptotic representations for importance-sampling estimators of value-at-risk and conditional value-at-risk

Value-at-risk (VaR) and conditional value-at-risk (CVaR) are important risk measures. They are often estimated by using importance-sampling (IS) techniques. In this paper, we derive the asymptotic representations for IS estimators of VaR and CVaR. Based on these representations, we are able to prove the consistency and asymptotic normality of the estimators and to provide simple conditions under which the IS estimators have smaller asymptotic variances than the ordinary Monte Carlo estimators.