基于回归组合技术的连续性抽样估计方法研究

在使用样本轮换的连续性抽样调查中,不仅可以利用前期调查的研究变量的信息,还可使用现期调查的辅助变量信息来建立回归模型进行回归估计,进而构造回归组合估计量,并在此基础上确定最优样本轮换率和最优权重系数,使得回归组合估计量的方差最小,从而更大程度地提高连续性抽样调查的估计精度。     

三维平衡多水平轮换设计及其连续性估计方法研究

 针对现行多水平轮换调查存在的一系列问题,本文提出三维平衡多水平轮换模式设计及其广义组合估计方法。在这套设计方法中,将各种偏差和两类相关关系引入到广义组合估计量公式中,提高了估计量的准确性,同时在多目标调查下还应用最优化方法确定一套最优系数,使得连续性的多目标调查的整体估计精度达到最高,同时又兼顾各类目标量的精度要求。这套系统化、理论化的设计方法将为我国未来开展多水平轮换调查提供理论指导。     

四分之一轮换面板下的稳健估计方法

文章从过度置信度视角考察了广义最小二乘估计量在四分之一轮换面板下产生的偏误问题,并提出了一种稳健估计方法来修正过高的过度置信度,进而提高估计精度。在一定的设计条件下,证明了修正后的估计量具有一致性和渐近正态分布特征等优良性质。模拟研究结果显示,与四分之一轮换面板下广义最小二乘估计量相比,提出的估计方法在保持相对偏差和均方误差基本不变的情况下,有效降低了过度置信度。     

二维平衡单水平轮换模式设计研究

现行的轮换样本调查使用各种类型的单水平轮换模式,在西方各国均得到了广泛应用,但是也存在着一系列问题。因此,通过对各种类型的轮换模式进行统一,并进行系统化、理论化研究,最终得出了二维平衡单水平轮换模式设计方法,并对其应用优势进行了总结。这套设计方法不仅将轮换模式设计与后续的估计方法研究统一起来,而且还能够削减各类轮换偏差的负面影响,并能准确度量轮换样本之间的相关关系,最终得出更加准确的连续性抽样估计量。     

分层抽样下的样本轮换理论研究

讨论用于回归估计的二相抽样理论在分层抽样下样本轮换后估计量的构造及其精度问题，并在构造的估计量的基础上计算了分层抽样下的最优样本轮换率，这对于深入研究分层抽样理论，使其估计量的精度提高，从而更好地实现抽样调查的目标有积极意义。     

多水平样本轮换调查及其组合估计方法

文章以两水平样本轮换为例,研究了连续性抽样调查中多水平样本轮换的问题.在多水平样本轮换模式下,不仅能够搜集固定的轮换样本在连续各期的信息,而且能够每一期更换新的轮换样本.文章还运用组合估计的思想.利用现期及过去各期的调查信息,分别构造出了每月总体情况、月度之间以及年度之间变化情况的组合估计量,并推导出了各类组合估计量的方差.     

OLS估计量:最优线性无偏估计的求证与推广

在大多数的统计学教材中,关于一元线性回归最小二乘估计量是总体回归系数的最优线性无偏估计量这个结论,给出证明的并不多,在一些计量经济学的著作中,虽然给出了证明,但是其过程和运用的数学技巧也令初学者望而却步,本文将运用大家耳熟能详的拉格朗日极值定理对该问题进行一个简单直观的证明,使大家对最优、线性、无偏等概念有一个更深刻的认识.     

连续性抽样调查中总体均值的估计

在连续性抽样调查中,利用前期信息和辅助信息可以大大提高估计精度,但是以往的估计量大多假设辅助信息总体均值已知,文章介绍一种在连续性抽样调查中,辅助信息总体均值未知的情况下,通过两阶段抽样,利用轮换样本方法和辅助变量信息,对总体均值进行估计的新的估计方法,并将新提出的估计量与原有的估计量进行比较,发现其精度更高,而且有利于减少调查成本。     

抽样调查中基于平衡样本的稳健预测

抽样调查中基于模型推断方法获得的估计量性质是依赖于模型的。在恰当的模型下比率估计和扩张估计是最优线性无偏估计。当模型设定错误时,比率估计和扩张估计是有偏估计,但如果样本是平衡的,可以消除偏倚,从而实现了复杂问题简单处理的思想。     

轮换样本调查的轮换模式设计与估计方法

文章以我国城市住户调查的轮换模式设计为例,研究了轮换样本调查中的轮换模式设计与估计方法等问题.不完全单水平轮换模式是轮换样本调查中非常理想的一种轮换模式,既吸收了单水平轮换模式的优点,又充分体现了轮换样本调查的优势.文章所研究的这套轮换模式设计与估计方法不仅适合在我国城市住户抽样调查中使用,而且也可推广应用到我国政府统计部门开展的其他类型的连续性抽样调查中.     

A note on optimal and robust spacing selection

The problem of quantile selection for the asymptotically best linear unbiased estimators of location and scale parameters is considered. The asymptotic properties of several quantile selection methods for simultaneous parameter estimation are derived and simple approximate solutions are provided. A robust scheme for quantile selection is also developed.     

Estimation of the Mean and Standard Deviation of the Logistic Distribution Based on Multiply Type-II Censored Samples

In this paper, we discuss the problem of estimating the mean and standard deviation of a logistic population based on multiply Type-II censored samples. First, we discuss the best linear unbiased estimation and the maximum likelihood estimation methods. Next, by appropriately approximating the likelihood equations we derive approximate maximum likelihood estimators for the two parameters and show that these estimators are quite useful as they do not need the construction of any special tables (as required for the best linear unbiased estimators) and are explicit estimators (unlike the maximum likelihood estimators which need to be determined by numerical methods). We show that these estimators are also quite efficient, and derive the asymptotic variances and covariance of the estimators. Finally, we present an example to illustrate the methods of estimation discussed in this paper.     

A comparison of estimation techniques for the three parameter pareto distribution

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.     

Best linear unbiased estimators of parameters of a simple linear regression model based on ordered ranked set samples

As an alternative to an estimation based on a simple random sample (BLUE-SRS) for the simple linear regression model, Moussa-Hamouda and Leone [E. Moussa-Hamouda and F.C. Leone, The o-blue estimators for complete and censored samples in linear regression, Technometrics, 16 (3) (1974), pp. 441–446.] discussed the best linear unbiased estimators based on order statistics (BLUE-OS), and showed that BLUE-OS is more efficient than BLUE-SRS for normal data. Using the ranked set sampling, Barreto and Barnett [M.C.M. Barreto and V. Barnett, Best linear unbiased estimators for the simple linear regression model using ranked set sampling. Environ. Ecoll. Stat. 6 (1999), pp. 119–133.] derived the best linear unbiased estimators (BLUE-RSS) for simple linear regression model and showed that BLUE-RSS is more efficient for the estimation of the regression parameters (intercept and slope) than BLUE-SRS for normal data, but not so for the estimation of the residual standard deviation in the case of small sample size. As an alternative to RSS, this paper considers the best linear unbiased estimators based on order statistics from a ranked set sample (BLUE-ORSS) and shows that BLUE-ORSS is uniformly more efficient than BLUE-RSS and BLUE-OS for normal data.     

Linear Estimators and Predictors Based on Generalized Order Statistics from Generalized Pareto Distributions

Linear estimation and prediction based on several samples of generalized order statistics from generalized Pareto distributions is considered. Representations of best linear unbiased estimators (BLUEs) and best linear equivariant estimators in location-scale families are derived, as well as corresponding optimal linear predictors. Moreover, we study positivity of the linear estimators of the scale parameter. An example illustrates that the BLUE may attain negative values with positive probability in certain situations.     

Nonlinear unbiased estimation in linear models †

In the paper the problem of nonlinear unbiased estimation of expectation in linear models is considered. The considerations are restricted to linear plus quadratic estimators with quadratic parts invariant under a group of translations. The one way classification model is considered in detail, for which an explicit formula for the locally best estimators is presented. A numerical evaluation of variances of the best estimators is given for some unbalanced one way classification models and compared with the variance of the ordinary linear estimators.     

Estimation of the location and scale parameters of the extreme value distmbution based on multiply type-II censored samples

In this paper, we consider the problem of estimating the location and scale parameters of an extreme value distribution based on multiply Type-II censored samples. We first describe the best linear unbiased estimators and the maximum likelihood estimators of these parameters. After observing that the best linear unbiased estimators need the construction of some tables for its coefficients and that the maximum likelihood estimators do not exist in an explicit algebraic form and hence need to be found by numerical methods, we develop approximate maximum likelihood estimators by appropriately approximating the likelihood equations. In addition to being simple explicit estimators, these estimators turn out to be nearly as efficient as the best linear unbiased estimators and the maximum likelihood estimators. Next, we derive the asymptotic variances and covariance of these estimators in terms of the first two single moments and the product moments of order statistics from the standard extreme value distribution. Finally, we present an example in order to illustrate all the methods of estimation of parameters discussed in this paper.     

Optimal estimation in rotation patterns

The aim of this paper is to examine the setting of surveys repeated over time when the elements in the sample are rotated in a predesigned way. On each occasion the best linear unbiased estimator (BLUE) of the current population mean, built on all past responses, is to be found. The most straightforward approach would be to compute the estimator as a solution of a least squares problem with linear restrictions. However, this method has certain drawbacks related to the fact that the size of the response data set increases over time. We follow a different approach based on finding linear recurrence relationships between optimal estimators obtained on successive occasions. Most of the original disadvantages are then corrected. In this context we present the solution to the BLUE estimation problem for some—sufficiently regular—classes of rotation patterns.     

Finite-population variance estimation under systematic sampling schemes with multiple random starts

Motivated by Sampath [Finite population variance estimation under LSS with multiple random starts, Commun. Statist. – Theory Methods 38 (2009), pp. 3596–3607], in this paper unbiased estimators for population variance have been developed under linear systematic sampling, balanced systematic sampling and modified systematic sampling with multiple random starts. Expressions for variances of the estimators are also developed. Detailed numerical comparative studies have been carried out to study the performances of the estimators under various systematic sampling schemes with multiple random starts and some interesting conclusions have been drawn out of the study.