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统计证据：似然范式AI 解读

The First Principle Introduction The Law of Likelihood Three Questions Towards Verification Relativity of Evidence Strength of Evidence Counterexamples Testing Simple Hypotheses Composite Hypotheses Another Counterexample Irrelevance of the Sample Space The Likelihood Principle Evidence and Uncertainty Summary Exercises Neyman-Pearson Theory Introduction Neyman-Pearson Statistical Theory Evidential Interpretation of Results of Neyman-Pearson Decision Procedures…

稳健似然AI 解读

Strong theoretical arguments imply that for directly representing and interpreting statistical data as evidence, the proper vehicle is the likelihood function. These arguments have had limited impact on statistical practice. One reason for this is that likelihood functions are explicitly model dependent and thus appear to be inherently nonrobust. In this article we examine the concept of robustness as it relates to likelihood functions. We note five ways that likelihood…

稳健似然AI 解读

Strong theoretical arguments imply that for directly representing and interpreting statistical data as evidence, the proper vehicle is the likelihood function. These arguments have had limited impact on statistical practice. One reason for this is that likelihood functions are explicitly model dependent and thus appear to be inherently nonrobust. In this article we examine the concept of robustness as it relates to likelihood functions. We note five ways that likelihood…

两阶段整群抽样中稳健方差估计的预测方法AI 解读

Robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two-stage cluster sample in which the first-stage sampling fraction is small. The analysis is based on prediction (superpopulation) models that allow for very general correlation structure within clusters. Results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters. Ratio, regression, and…

两阶段整群抽样中稳健方差估计的预测方法AI 解读

Robust statistics are derived for estimating the error variance when a finite population total or a ratio of totals is estimated from a two-stage cluster sample in which the first-stage sampling fraction is small. The analysis is based on prediction (superpopulation) models that allow for very general correlation structure within clusters. Results are obtained for when all cluster sizes are known and for when sizes are known only for sample clusters. Ratio, regression, and…

有限总体置信区间的条件覆盖性质AI 解读

Standardized errors (Ť — T)/v 1/2 were calculated for both ratio and regression estimators in each of 10,000 simple random samples of n = 32 from each of six populations, using four different variance estimators. Graphs show how the percentage of intervals T ± 1.96 v 1/2 that fail to contain T changes as a function of the average value of the auxiliary variable in the sample. They reveal that (a) intervals using the variance estimators from standard linear regression theory…

摘要暂缺

有限总体抽样中的平衡样本与稳健贝叶斯推断AI 解读

Bayesian inference in finite populations uses probability models at two stages: (i) to describe relationships among population units and (ii) to express uncertainty concerning the values of parameters appearing at stage (i). Here we consider the Bayes posterior distribution of the population total when a multivariate nornxal regression model is used at stage (i), with a diffuse prior distribution on the regression coefficients. We study the situation where the stage (i)…

有限总体线性回归估计量及其方差估计的经验研究AI 解读

The usual variance estimator for the linear regression estimator of a finite population total is examined under some prediction (superpopulation) models. Its bias is compared with that of the least squares variance estimator. Also described are three bias-robust alternatives, one of which is the jackknife variance estimator. The theoretical results are supported by an empirical study in which simple and restricted random samples as well as some purposive (nonrandom) samples…

摘要暂缺

比率估计量及其方差估计量的实证研究AI 解读

This paper reports results from an empirical study of the ratio estimator for a finite population total. From each of six real populations, 1,000 simple random samples, 1,000 restricted random samples, and three nonrandom samples of size 32 are drawn. Performance of the ratio estimator and of five estimators of its variance is compared with theoretical results generated using (a) prediction (superpopulation) models and (b) probability sampling distributions. The results,…

有限总体抽样中的方差估计AI 解读

Under a linear regression model, the best linear unbiased estimator (BLUE) for a finite population total can be obtained. The problem studied here is that of estimating the variance for setting large-sample confidence intervals about the BLUE when the model generating this estimate is inaccurate. A robust variance estimator is derived, and its asymptotic properties are shown to compare favorably with those of the weighted least-squares variance estimator. The robust variance…

有限总体抽样理论中的似然函数AI 解读

Both conventional randomization models and prediction, i.e. superpopulation, models for finite populations are discussed from the viewpoint of the likelihood axiom. It is argued that finite populations do fall within the scope of this axiom, and that the likelihood function, when properly defined and interpreted, can play the same fundamental role in finite population theory as it does elsewhere in statistical inference. Under a multivariate normal regression model, the…

两阶段抽样的线性最小二乘预测方法AI 解读

The linear least-squares prediction approach is applied to some problems in two-stage sampling from finite populations. A theorem giving the optimal (BLU) estimator and its error-variance under a general linear “superpopulation” model for a finite population is stated. This theorem is then applied to a model describing many populations whose elements are grouped naturally in clusters. Next, the probability model is used to analyze various conventional estimators and certain…

有限总体抽样理论中的似然函数AI 解读

Both conventional randomization models and prediction, i.e. superpopulation, models for finite populations are discussed from the viewpoint of the likelihood axiom. It is argued that finite populations do fall within the scope of this axiom, and that the likelihood function, when properly defined and interpreted, can play the same fundamental role in finite population theory as it does elsewhere in statistical inference. Under a multivariate normal regression model, the…

有限总体中的稳健估计（二）：按规模变量分层AI 解读

It has been established in Part I [3] that for estimating a finite population total, the estimators which are optimal under simple super-population models can be made insensitive to certain departures from the models by the choice of balanced samples. Here stratification on a size variable is considered as another technique for protecting against model failure. Together the two techniques, stratification and balanced sampling, are shown to provide more efficient protection…

有限总体中的稳健估计（一）AI 解读

This is an application of a least-squares prediction approach to finite population sampling theory. One way in which this approach differs from the conventional one is its focus on characteristics of particular samples rather than on plans for choosing samples. Here we study samples in which many superpopulation models lead to the same optimal (BLU) estimator. Random sampling is considered in the light of these results.

It has been established in Part I [3] that for estimating a finite population total, the estimators which are optimal under simple super-population models can be made insensitive to certain departures from the models by the choice of balanced samples. Here stratification on a size variable is considered as another technique for protecting against model failure. Together the two techniques, stratification and balanced sampling, are shown to provide more efficient protection…

特定线性回归模型下的有限总体抽样理论AI 解读

Problems of estimating totals in finite populations, when auxiliary information regarding variate values is available, are considered under some linear regression, ‘ super-population’, models. Optimal strategies involving linear estimators are derived under certain variance assumptions and compared under various assumptions. For a model which seems to apply in many practical problems, the conventional ratio estimator is shown to be, in a certain natural sense, optimal, but…

若干线性回归模型下的有限总体抽样理论AI 解读

SUMMARY Problems of estimating totals in finite populations, when auxiliary information regarding variate values is available, are considered under some linear regression, 'super-population', models. Optimal strategies involving linear estimators are derived under certain variance assumptions and compared under various assumptions. For a model which seems to apply in many practical problems, the conventional ratio estimator is shown to be, in a certain natural sense,…