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热卡插补调查数据的 Jackknife 方差估计AI 解读

Hot deck imputation is commonly employed for item nonresponse in sample surveys. It is also a common practice to treat the imputed values as if they are true values, and then compute the variance estimates using standard formulae. This procedure, however, could lead to serious underestimation of the true variance, when the proportion of missing values for an item is appreciable. We propose a jackknife variance estimator for stratified multistage surveys which is obtained by…

热卡插补调查数据的刀切法方差估计AI 解读

Hot deck imputation is commonly employed for item nonresponse in sample surveys. It is also a common practice to treat the imputed values as if they are true values, and then compute the variance estimates using standard formulae. This procedure, however, could lead to serious underestimation of the true variance, when the proportion of missing values for an item is appreciable. We propose a jackknife variance estimator for stratified multistage surveys which is obtained by…

加性模型下相关响应方差的“最优”估计AI 解读

Additive models are often employed to measure the impact of response errors on the accuracy of survey estimates. An important feature of these models is that the correlated errors from specified error sources, such as interviewers and coders, contribute additive components, called correlated response variance (CRV) components, to the total variance of a survey estimator. As a result of these correlated components, the usual estimators of variance of a mean or a total are…

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摘要暂缺

小区域估计量的均方误差估计AI 解读

Small-area estimation has received considerable attention in recent years because of a growing demand for reliable small-area statistics. The direct-survey estimators, based only on the data from a given small area (or small domain), are likely to yield unacceptably large standard errors because of small sample size in the domain. Therefore, alternative estimators that borrow strength from other related small areas have been proposed in the literature to improve the…

利用辅助信息估计调查数据的分布函数与分位数AI 解读

SUMMARY Ratio and difference estimators of a population distribution function under a general sampling design are obtained, using auxiliary population information. The relative mean errors and relative mean square errors of these estimators and a model-based estimator of Chambers & Dunstan (1986) are compared through a simulation study. The advantages of the design-based estimators over the model-based estimator under model misspecifications, especially for large samples,…

复杂调查数据的重采样推断AI 解读

Methods for standard errors and confidence intervals for nonlinear statistics —such as ratios, regression, and correlation coefficients—have been extensively studied for stratified multistage designs in which the clusters are sampled with replacement, in particular, the important special case of two sampled clusters per stratum. These methods include the customary linearization (or Taylor) method and resampling methods based on the jackknife and balanced repeated replication…

摘要暂缺

For testing the goodness-of-fit of a $\log$-linear model to a multi-way contingency table with cell proportions estimated from survey data, Rao and Scott (1984) derived a first-order correction, $\delta\ldot$, to Pearson chi-square statistic, $X^2$ (or the likelihood ratio statistic, $G^2$) that takes account of the survey design. It was also shown that $\delta\ldot$ requires the knowledge of only the cell design effects (deffs) and the marginal deffs provided the model…

摘要暂缺

ANOVA 模型中渐近无偏非负二次方差分量估计的存在性AI 解读

Conditions for the existence of asymptotically unbiased, nonnegative quadratic estimates of individual variance components in general ANOVA models are investigated. A simple necessary condition for general models is obtained. Necessary and sufficient conditions are obtained in the case of random, balanced nested classification models and the random unbalanced one-way model. The investigation demonstrates the need for exercising caution when employing nonnegative quadratic…

分层样本推断：非线性统计量三种方法的二阶分析AI 解读

For stratified samples and nonlinear statistics that can be expressed as functions of estimated totals, second-order asymptotic expansions of the linearization, jackknife, and balanced repeated-replication variance estimators are obtained. Based on these, comparisons are made in terms of their biases. Some higher order asymptotic equivalence results are also established. The special case of a combined ratio estimator is investigated in detail. Some results on bias reduction…

多阶段抽样设计中简化的无偏方差估计AI 解读

All unequal probability selection methods of two first-stage units per stratum are shown to permit the use of a grouping device, leading to simplified unbiased variance estimators in multistage sampling. These variance estimators avoid the calculation of within first-stage components with a high probability. Several desirable properties of the grouping method are established. Empirical results on efficiencies of ‘grouping’ estimators and stabilities of corresponding variance…

调查数据估计单元比例时多维列联表的卡方检验AI 解读

The impact of survey design on standard multinomial-based methods for a multiway contingency table is studied, under nested loglinear models. The asymptotic null distribution of the Pearson chi-squared test statistic, $X^2$ (or the likelihood ratio test statistic, $G^2$) is obtained as a weighted sum of independent $\chi^2_1$ random variables, and the weights are then related to the familiar design effects (deffs) used by survey samplers. A simple correction to $X^2$ (or $G^2$…

多阶段抽样设计中的简化无偏方差估计AI 解读

All unequal probability selection methods of two first-stage units per stratum are shown to permit the use of a grouping device, leading to simplified unbiased variance estimators in multistage sampling. These variance estimators avoid the calculation of within first-stage components with a high probability. Several desirable properties of the grouping method are established. Empirical results on efficiencies of ‘grouping’ estimators and stabilities of corresponding variance…

分层样本推断：线性化、刀切法与平衡重复复制法的性质AI 解读

The asymptotic normality of both linear and nonlinear statistics and the consistency of the variance estimators obtained using the linearization, jackknife and balanced repeated replication (BRR) methods in stratified samples are established. The results are obtained as $L \rightarrow \infty$ within the context of a sequence of finite populations $\{\Pi_L\}$ with $L$ strata in $\Pi_L$ and are valid for any stratified multistage design in which the primary sampling units…

复杂抽样分类数据分析：拟合优度与二维表独立性的卡方检验AI 解读

The effect of stratification and clustering on the asymptotic distributions of standard Pearson chi-squared test statistics for goodness of fit (simple hypothesis) and independence in a two-way contingency table, denoted as X 2 and XI 2, respectively, is investigated. It is shown that both X 2 and XI 2 are asymptotically distributed as weighted sums of independent χ1 2 random variables. The weights are then related to the familiar design effects (deffs) used by survey…

可能具有不同方差的正态总体共同均值估计：模拟研究AI 解读

Relative efficiency of estimators of the common mean of possibly different normal populations N(μ, σ i 2) is investigated empirically. A weighted least squares estimator , with weights based on a modification of minimum norm quadratic unbiased (MINQU) estimators of the σ i 2, is found to be substantially more efficient than the maximum likelihood (ML) estimator of μ when the heterogeneity in the σ i , is small to moderate and the number of sample observations from a…

可能具有不同方差的正态总体共同均值估计：模拟研究AI 解读

Relative efficiency of estimators of the common mean of possibly different normal populations N(μ, σ i 2) is investigated empirically. A weighted least squares estimator , with weights based on a modification of minimum norm quadratic unbiased (MINQU) estimators of the σ i 2, is found to be substantially more efficient than the maximum likelihood (ML) estimator of μ when the heterogeneity in the σ i , is small to moderate and the number of sample observations from a…

未知对角协方差矩阵下的线性回归估计AI 解读

A method of estimating the parameters of a linear regression model when the covariance matrix is an unknown diagonal matrix is investigated. It is assumed that the observations fall into $k$ groups with constant error variance for a group. The estimation is carried out in two steps, the first step being an ordinary least squares regression. The least squares residuals are used to estimate the covariance matrix and the second step is the calculation of the generalized least…

按总规模比例抽样中的方差估计AI 解读

The problem of estimating the variance of the ratio estimator in sampling with probability proportional to aggregate size is investigated. The form of nonnegative unbiased variance estimators is found. For sample size n = 2, it is shown that there is at most one nonnegative unbiased variance estimator, whereas for n > 2, two different, possibly nonnegative, unbiased variance estimators are proposed. The performance of the proposed unbiased variance estimators, as regards…

用于分层与分析性调查的双重抽样AI 解读

SUMMARY A simple method of double sampling for stratification is proposed and the classical nonresponse theory is obtained as a special case. The method leads to simple solutions for the optimal design of analytical surveys involving comparison of group means, when the groups are not identifiable in advance.