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??How to solve the inference problem of candidate database web surveys is an urgent problem to be solved in the development of web survey. In order to solve this problem, the inference method of non-probability sampling based on superpopulation pseudo design and the combined sample is proposed. A superpopulation model is firstly built up to construct pseudo weights for a survey sample of the web candidate database. The estimator of the population mean is then computed according to the combined sample composed of the survey sample of the web candidate database and a probability sample. The variance estimator of the population mean estimator is lastly derived according to the variance estimation theory of the superpopulation model. The Bootstrap and Jackknife methods are also used to compute the variance estimator. And all these variance estimation methods are compared. The research results show that the population mean estimator based on superpopulation pseudo design and the combined sample is better, and has higher efficiency than the estimator only using the probability sample and the weighted estimator only using the survey sample of the web candidate database. The variance estimator computed by using the VM1, VM2 and VM3 method are relatively better.     

Model-based design in small area estimation

In this paper, we address the problem of an efficient estimation strategy when solving real survey sampling problems. We consider the panel data model with random effects as a superpopulation model. We investigate the performance of model-assisted estimators under model-based sample designs in a simulation experiment based on the real data (Lithuanian survey on short-term statistics on service) taken as a true population. Here the model-based sampling refers to a sample design constructed using the model and information about the behavior of the model-assisted estimator on available auxiliary data.     

Comparison of variance estimators for the ratio estimator based on small sample

1. Introduction and Main ResultsSuppose the population of interest consists of N distinct units labelled by 1,' f N.Associated with unit i are two values K and Xi, with Xi > 0 (i = 1,' t N). Denote thepopulation means of K and X, by Y and X respectively. To estimate Y, it is customaryto select a simple raPdom sample of size n and to use the ratio estimatNn = RX if Xis available, where R = y/x is an estimator for population ratio R = Y/X, y and x arerespectively the 8ample mean8 of…     

长沙市规模以下零售业抽样调查方案

本文介绍了一个根据具体城市情况制定的零售贸易餐饮业的抽样调查方案.以长沙市规模以下零售业、餐饮业为总体,用区域抽样代替一般的名录抽样,并采用细致的分层解决商业单位分布不均匀问题.文中也给出了与抽样方案配套的总体和域目标量的估计及相应的方差估计公式.     

抽样调查中多个指标值的同时估计

本文在ＥＶ（Ｅｒｏｒ ｉｎ Ｖａｒｉａｂｌｅｓ）超总体模型下讨论有限总体两个指标值的同时估计问题，证明了样本均值作为整体均值的估计在均方差阵最小的意义下是最优的．     

An adjusted maximum likelihood method for solving small area estimation problems

For the well-known Fay-Herriot small area model, standard variance component estimation methods frequently produce zero estimates of the strictly positive model variance. As a consequence, an empirical best linear unbiased predictor of a small area mean, commonly used in small area estimation, could reduce to a simple regression estimator, which typically has an overshrinking problem. We propose an adjusted maximum likelihood estimator of the model variance that maximizes an adjusted likelihood defined as a product of the model variance and a standard likelihood (e.g., a profile or residual likelihood) function. The adjustment factor was suggested earlier by Carl Morris in the context of approximating a hierarchical Bayes solution where the hyperparameters, including the model variance, are assumed to follow a prior distribution. Interestingly, the proposed adjustment does not affect the mean squared error property of the model variance estimator or the corresponding empirical best linear unbiased predictors of the small area means in a higher order asymptotic sense. However, as demonstrated in our simulation study, the proposed adjustment has a considerable advantage in small sample inference, especially in estimating the shrinkage parameters and in constructing the parametric bootstrap prediction intervals of the small area means, which require the use of a strictly positive consistent model variance estimate.     

批发零售贸易业、餐饮业抽样调查方案及数据处理方法

本文介绍我国批发零售贸易业、餐饮业调查的抽样方案,方案以省为总体,区县为初级抽样单元,为满足对部分地市(域)估计的需要,对区县的抽样考虑了不放回样本追加。文中也给出了与抽样方案配套的总体和域目标量的估计及相应的方差估计公式。     

Imputation of mean of ratios for missing data and its application to PPSWR sampling

In practical survey sampling, nonresponse phenomenon is unavoidable. How to impute missing data is an important problem. There are several imputation methods in the literature. In this paper, the imputation method of the mean of ratios for missing data under uniform response is applied to the estimation of a finite population mean when the PPSWR sampling is used. The imputed estimator is valid under the corresponding response mechanism regardless of the model as well as under the ratio model regardless of the response mechanism. The approximately unbiased jackknife variance estimator is also presented. All of these results are extended to the case of non-uniform response. Simulation studies show the good performance of the proposed estimators.     

Varying coefficients partially linear models with randomly censored data

This paper considers the problem of estimation and inference in semiparametric varying coefficients partially linear models when the response variable is subject to random censoring. The paper proposes an estimator based on combining inverse probability of censoring weighting and profile least squares estimation. The resulting estimator is shown to be asymptotically normal. The paper also proposes a number of test statistics that can be used to test linear restrictions on both the parametric and nonparametric components. Finally, the paper considers the important issue of correct specification and proposes a nonsmoothing test based on a Cramer von Mises type of statistic, which does not suffer from the curse of dimensionality, nor requires multidimensional integration. Monte Carlo simulations illustrate the finite sample properties of the estimator and test statistics.     

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。     

Optimal variance estimation based on lagged second-order difference in nonparametric regression

Differenced estimators of variance bypass the estimation of regression function and thus are simple to calculate. However, there exist two problems: most differenced estimators do not achieve the asymptotic optimal rate for the mean square error; for finite samples the estimation bias is also important and not further considered. In this paper, we estimate the variance as the intercept in a linear regression with the lagged Gasser-type variance estimator as dependent variable. For the equidistant design, our estimator is not only \(n^{1/2}\)-consistent and asymptotically normal, but also achieves the optimal bound in terms of estimation variance with less asymptotic bias. Simulation studies show that our estimator has less mean square error than some existing differenced estimators, especially in the cases of immense oscillation of regression function and small-sized sample.     

基于轮换样本连续性调查的校准组合估计方法研究

校准估计是抽样调查中比较常用的一种利用辅助信息提高估计量精度的方法。回归组合估计量作为轮换样本连续性调查中使用的一种有效的估计量,是可以通过校准程序得到的。基于回归组合估计量和校准程序之间的关系,本文提出了轮换样本连续性抽样调查条件下的不同校准组合估计量及其方差估计。校准组合估计量的主要思想是在校准估计程序中将拼配样本和非拼配样本的辅助信息进行不同的组合利用。本文利用美国现时人口调查的微观数据进行数值模拟,来比较不同校准组合估计量的估计效率,模拟结果表明两步校准组合估计量和两步校准双组合估计量的表现相似,且估计精度都高于H-T估计量及回归组合估计量;而两步校准组合估计量由于其简便性更适合应用于实践中。最后以我国农村住户连续性抽样调查为例,设计一套符合我国实际的轮换样本连续性调查方案,并将提出的校准组合估计量运用于估计阶段,为中国政府统计调查提供一定的借鉴和参考.     

Probability density estimation with surrogate data and validation sample

The probability density estimation problem with surrogate data and validation sample is considered. A regression calibration kernel density estimator is defined to incorporate the information contained in both surrogate variates and validation sample. Also, we define two weighted estimators which have less asymptotic variances but have bigger biases than the regression calibration kernel density estimator. All the proposed estimators are proved to be asymptotically normal. And the asymptotic representations for the mean squared error and mean integrated square error of the proposed estimators are established, respectively. A simulation study is conducted to compare the finite sample behaviors of the proposed estimators.     

Estimation of intrinsic growth factors in a class of stochastic population model

This article discusses the problem of parameter estimation with nonlinear mean-reversion type stochastic differential equations (SDEs) driven by Brownian motion for population growth model. The estimator in the population model is the climate effects, population policy and environmental circumstances which affect the intrinsic rate of growth r. The consistency and asymptotic distribution of the estimator θ is studied in our general setting. In the calculation method, unlike previous study, since the nonlinear feature of the model, it is difficult to obtain an explicit formula for the estimator. To solve this, some criteria are used to derive an asymptotically consistent estimator. Furthermore Girsanov transformation is used to simplify the equations, which then gives rise to the corresponding convergence of the estimator being with respect to a family of probability measures indexed by the dispersion parameter, while in the literature the existing results have dealt with convergence with respect to a given probability measure.     

复杂设计下类均值复制与类加权均值复制的比较（英文）

复制数据是处理抽样调查中数据项目缺失的一种常用方法。在两种常见模型及复杂抽样设计下，本文对处理数据项目缺失的类均值复制和类加权均值复制方法进行了对比。     

A Computationally Motivated Definition Of Parametric Estimation And Its Applications To The Gaussian Distribution

We introduce a treatment of parametric estimation in which optimality of an estimator is measured in probability rather than in variance (the measure for which the strongest general results are known in statistics). Our motivation is that the quality of an approximation algorithm is measured by the probability that it fails to approximate the desired quantity within a set tolerance. We concentrate on the Gaussian distribution and show that the sample mean is the unique “best” estimator, in probability, for the mean of a Gaussian distribution. We also extend this method to general penalty functions and to multidimensional spherically symmetric Gaussians. The algorithmic significance of studying the Gaussian distribution is established by showing that determining the average matching size in a graph is #P-hard, and moreover approximating it reduces to estimating the mean of a random variable that (under some mild conditions) has a distribution closely approximating a Gaussian. This random variable is (essentially) polynomial time samplable, thereby yielding an FPRAS for the problem.     

超总体模型下有限总体的估计

超总体模型是抽样理论与统计学其它分支联系的桥梁,借助于超总体模型研究抽样理论是一个有前途的方法．本文综述了这方面的结果,包括总体目标量的估计及其精度估计,同时提出了若干未来的研究问题．     

Asymptotic theory of parameter estimation by a contrast function based on interpolation error

Interpolation is an important issue for a variety fields of statistics (e.g., missing data analysis). In time series analysis, the best interpolator for missing points problem has been investigated in several ways. In this paper, the asymptotics of a contrast function estimator defined by pseudo interpolation error for stationary process are investigated. We estimate parameters of the process by minimizing the pseudo interpolation error written in terms of a fitted parametric spectral density and the periodogram based on observed stretch. The estimator has the consistency and asymptotical normality. Although the criterion for the interpolation problem is known as the best in the sense of smallest mean square error for past and future extrapolation, it is shown that the estimator is asymptotically inefficient in general parameter estimation, which leads to an unexpected result.     

Statistical analysis of hierarchical stochastic models: Examples and approaches

This paper introduces and illustrates the concept of hierarchical or random parameter stochastic process models. These models arise when members of a population each generate a stochastic process governed by certain parameters and the values of the parameters may be viewed as single realizations of random variables. The paper treats the estimation of the individual parameter values and the parameters of the superpopulation distribution. Examples from system reliability, pharmacokinetic compartment models, and criminal careers are introduced; a reliability (Poisson process-exponential interval) process is examined in greater detail. An explicit, approximate, robust estimator of individual (log) failure rates is presented for the case of a long-tailed (Studentt) superpopulation. This estimator exhibits desirable limited shrinkage properties, refusing to borrow unjustified strength. Numerical properties of such estimators are described more fully elsewhere.     

Numerical approximation of conditional asymptotic variances using Monte Carlo simulation

We consider in this paper the use of Monte Carlo simulation to numerically approximate the asymptotic variance of an estimator of a population parameter. When the variance of an estimator does not exist in finite samples, the variance of its limiting distribution is often used for inferences. However, in this case, the numerical approximation of asymptotic variances is less straightforward, unless their analytical derivation is mathematically tractable. The method proposed does not assume the existence of variance in finite samples. If finite sample variance does exist, it provides a more efficient approximation than the one based on the convergence of finite sample variances. Furthermore, the results obtained will be potentially useful in evaluating and comparing different estimation procedures based on their asymptotic variances for various types of distributions. The method is also applicable in surveys where the sample size required to achieve a fixed margin of error is based on the asymptotic variance of the estimator. The proposed method can be routinely applied and alleviates the complex theoretical treatment usually associated with the analytical derivation of the asymptotic variance of an estimator which is often managed on a case by case basis. This is particularly appealing in view of the advance of modern computing technology. The proposed numerical approximation is based on the variances of a certain truncated statistic for two selected sample sizes, using a Richardson extrapolation type formulation. The variances of the truncated statistic for the two sample sizes are computed based on Monte Carlo simulations, and the theory for optimizing the computing resources is also given. The accuracy of the proposed method is numerically demonstrated in a classical errors-in-variables model where analytical results are available for the purpose of comparisons.