正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测．本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测．     

正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测.本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测.     

有限总体中基于广义Liu 估计的预测及其小样本性质

在有限总体中提出了一类基于广义Liu估计的新的预测,得到了基于广义Liu估计的预测在预测均方误差意义下优于最优线性无偏预测的充要条件,并通过实例对理论成果进行了进一步的说明.     

二次损失下任意秩有限总体中的线性Minimax预测

本文对通常的二次损失作了适当的修改,在此基础上研究了一个预测在齐次线性预测函数类中的极大极小性.得到了任意秩有限总体中线性可预测变量的唯一线性Minimax预测(有关唯一性在几乎处处意义下理解).     

二次损失下任意秩有限总体中的线性Minimax预测

本文对通常的二次损失作了适当的修改,在此基础上研究了一个预测在齐次线性预测函数类中的极大极小性。得到了任意秩有限总体中线性可预测变量的唯一线性Minimax预测(有关唯一性在几乎处处意义下理解)。     

线性等式约束下有限总体中的最优预测

本研究了带线性等式的约束条件的有限总体中的最优预测问题,给出了条件可预测变量和条件最优线性无偏测的定义,得到了条件可预测变量的所有条件最优线性无偏预测,并证明了它在几乎处处意义下的唯一性。     

任意秩有限总体中的简单投影预测

本文得到了任意秩有限总体中的简单投影预测为最优预测的充要条件 ,并研究了简单投影预测关于协方差矩阵的稳健性     

利用样本分位数的Logistic总体分布参数的近似最佳线性无偏估计

Harter H_L.,Balakrishnan N.等先后讨论了Logistic总体分布参数的极大似然估计,近似极大似然估计;其后Ogawa J.,Lloyd E.H.,Kulldorff G.,Gupta S.S,及chan L.K. 等又先后讨论了Logistlic分布参数的最佳线性无偏估计及估计的相对效率等问题.令人遗憾的是:在大样本情形下,上述估计均难以求得.为缓解这一困难,本文讨论利用样本分位数的Logistic总体的近似最佳线性无偏估计,给出估计量的大样本性质,以及样本分位数不超过10情形下,估计量有渐近最大相对估计效率时样本分位数的选取方案等.     

有限总体中的最优预测

研究了有限总体中的最优预测问题,在一般Ｇａｕｓｓ－Ｍａｒｋｏｖ模型下得到了线性可预测变量的最优线性无偏预测,特别地,考虑了一类特殊的预测函数：ｂ－线性预测函数。     

最小范数二次无偏估计与最小方差二次无偏估计的关系

本文给出了当V0 ≥ 0时 ,c′σ2 在混合模型M =( y ,Xβ ,Uξ,σ20 V0 )下的最小范数二次无偏估计的表达式及其证明 ;得到了当 y服从正态分布时 ,c′σ2 的最小范数二次无偏估计与其最小方差二次无偏估计之间的关系。     

Quadratic prediction and quadratic sufficiency in finite populations

The problem of quadratic prediction for population quadratic quantities in finite populations has been considered in the literature. In this paper, we mainly aim at extending the ordinary quadratic prediction problems to a general case, and derive the representations of the two essentially unique optimal predictors: one is an optimal invariant quadratic unbiased predictor, and the other is an optimal invariant quadratic (potentially) biased predictor. Further, we show that the two predictors are nonnegative and reasonable by considering an extreme situation, and apply resulting conclusions to a special model with a compound symmetric variance matrix. In addition, we propose a notion of quadratic sufficiency with regard to the optimal prediction problems by employing materials derived in the first part, and investigate corresponding characterizations in detail.     

Unbiased estimation of finite population variance using auxiliary information

Unbiased estimates, using auxiliary information, are developed for finite population variance.     

测量误差数据下线性模型的几乎无偏岭估计

文章讨论带测量误差的线性模型中参数估计的问题.当带测量误差的线性模型存在复共线的时候,通过几乎无偏估计的思想,提出了几乎无偏岭估计,并对估计的性质进行分析.通过研究发现几乎无偏岭估计不但能克服复共线性,同时有比较小的均方误差.     

Multivariate time series modeling,estimation and prediction of mortalities

We introduce a mixed regression model for mortality data which can be decomposed into a deterministic trend component explained by the covariates age and calendar year, a multivariate Gaussian time series part not explained by the covariates, and binomial risk. Data can be analyzed by means of a simple logistic regression model when the multivariate Gaussian time series component is absent and there is no overdispersion. In this paper we rather allow for overdispersion and the mixed regression model is fitted to mortality data from the United States and Sweden, with the aim to provide prediction and intervals for future mortality and annuity premium, as well as smoothing historical data, using the best linear unbiased predictor. We find that the form of the Gaussian time series has a large impact on the width of the prediction intervals, and it poses some new questions on proper model selection.     

Prediction with measurement errors in finite populations

We address the problem of selecting the best linear unbiased predictor (BLUP) of the latent value (e.g., serum glucose fasting level) of sample subjects with heteroskedastic measurement errors. Using a simple example, we compare the usual mixed model BLUP to a similar predictor based on a mixed model framed in a finite population (FPMM) setup with two sources of variability, the first of which corresponds to simple random sampling and the second, to heteroskedastic measurement errors. Under this last approach, we show that when measurement errors are subject-specific, the BLUP shrinkage constants are based on a pooled measurement error variance as opposed to the individual ones generally considered for the usual mixed model BLUP. In contrast, when the heteroskedastic measurement errors are measurement condition-specific, the FPMM BLUP involves different shrinkage constants. We also show that in this setup, when measurement errors are subject-specific, the usual mixed model predictor is biased but has a smaller mean squared error than the FPMM BLUP which points to some difficulties in the interpretation of such predictors.     

Toward anisotropic mesh construction and error estimation in the finite element method

Directional, anisotropic features like layers in the solution of partial differential equations can be resolved favorably by using anisotropic finite element meshes. An adaptive algorithm for such meshes includes the ingredients Error estimation and Information extraction/Mesh refinement. Related articles on a posteriori error estimation on anisotropic meshes revealed that reliable error estimation requires an anisotropic mesh that is aligned with the anisotropic solution. To obtain anisotropic meshes the so‐called Hessian strategy is used, which provides information such as the stretching direction and stretching ratio of the anisotropic elements. This article combines the analysis of anisotropic information extraction/mesh refinement and error estimation (for several estimators). It shows that the Hessian strategy leads to well‐aligned anisotropic meshes and, consequently, reliable error estimation. The underlying heuristic assumptions are given in a stringent yet general form. Numerical examples strengthen the exposition. Hence the analysis provides further insight into a particular aspect of anisotropic error estimation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 625–648, 2002; DOI 10.1002/num.10023     

On the distribution of sample mean in finite populations. I

We obtain Bergström-type [2] asymptotic expansions for sample mean in finite population [8]. Analogues of the Cornish-Fisher transformation are obtained in the cases of limit distributions from class $\mathcal{L}$ and distributions of sums of independent identically distributed random variables (in [2], the Bergström equality is used).     

排序集抽样下Inverse Rayleigh分布的Fisher信息量及其在参数估计中的应用

文章分别在简单随机抽样和排序集抽样下研究了Inverse Rayleigh分布中对应样本所含刻度参数θ的Fisher信息量.数值结果表示,同等样本容量的排序集样本比简单随机样本提供更多关于θ的信息.接着分别基于简单随机样本和排序集样本构造了θ的一些优良估计,并对估计结果进行了数值比较.     

On the relationship between finite volume and finite element methods applied to the Stokes equations

We investigate the relationship between finite volume and finite element approximations for the lower‐order elements, both conforming and nonconforming for the Stokes equations. These elements include conforming, linear velocity‐constant pressure on triangles, conforming bilinear velocity‐constant pressure on rectangles and their macro‐element versions, and nonconforming linear velocity‐constant pressure on triangles and nonconforming rotated bilinear velocity‐constant pressure on rectangles. By applying the relationship between the two methods, we obtain the convergence finite volume solutions for the Stokes equations. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 440–453, 2001.