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小区域估计的经验自助偏差校正与预测均方误差估计AI 解读

We develop a method for bias correction, which models the error of the target estimator as a function of the corresponding estimator obtained from bootstrap samples, and the original estimators and bootstrap estimators of the parameters governing the model fitted to the sample data. This is achieved by considering a number of plausible parameter values, generating a pseudo original sample for each parameter and bootstrap samples for each such sample, and then searching for…

小区域估计中贝叶斯与频率学派的误差度量AI 解读

Summary This paper compares analytically and empirically the frequentist and Bayesian measures of error in small area estimation. The model postulated is the nested error regression model which allows for random small area effects to represent the joint effect of small area characteristics that are not accounted for by the fixed regressor variables. When the variance components are known, then, under a uniform prior for the regression coefficients and normality of the error…

多层模型中不等选择概率的加权处理AI 解读

Summary When multilevel models are estimated from survey data derived using multistage sampling, unequal selection probabilities at any stage of sampling may induce bias in standard estimators, unless the sources of the unequal probabilities are fully controlled for in the covariates. This paper proposes alternative ways of weighting the estimation of a two-level model by using the reciprocals of the selection probabilities at each stage of sampling. Consistent estimators…

Gauss–Markov 定理向随机回归系数情形的扩展AI 解读

SUMMARY Several theorems which extend the Gauss-Markov theorem to the case of stochastic vectors of coefficients are presented in the literature. Some of these theorems, although differently formulated and proved, are based on the same assumptions and arrive at similar results. Some theorems are special cases of theorems, already existing in the literature. In other cases, theorems, which appear to be similar in their underlying assumptions and conclusions, differ in ways…