Variance Estimation for the Regression Estimator in Two-Phase Sampling
研究两阶段抽样中回归估计量的方差估计方法，比较了线性化、刀切法和自助法方差估计量的设计一致性和重复抽样性质，发现线性化估计量无条件性质更优，而刀切法及其线性化版本条件性质更好。
Abstract Many techniques in survey sampling depend on the possession of information about an auxiliary variable x, or a vector of auxiliary variables, available for the entire population. Regression estimates require , the population mean. If such information is unavailable, then one can sometimes obtain a large preliminary sample of xi relatively cheaply and use this to obtain a good estimate, say , of A smaller subsample can then be taken and the characteristic of interest, yi , measured. A regression estimator can then be used treating as if it were This is termed double sampling, or two-phase sampling. This article focuses on variance estimators for the regression estimator in the aforementioned context and their use in constructing confidence intervals. A design-based linearization variance estimator that makes more complete use of the sample data than the standard one is considered for two-phase sampling. A jackknife variance estimator and its linearized version are obtained and shown to be design consistent. A bootstrap variance estimator is also shown to be design consistent. Unconditional and conditional repeated sampling properties of these variance estimators are studied through simulation. It is shown that the linearization variance estimator displays superior unconditional properties, but the jackknife and its linearized version perform better conditionally.