We develop asymptotic theory for weighted likelihood estimators (WLE) under two-phase stratified sampling without replacement. We also consider several variants of WLEs involving estimated weights and calibration. A set of empirical process tools are developed including a Glivenko-Cantelli theorem, a theorem for rates of convergence of M-estimators, and a Donsker theorem for the inverse probabi...

Large sample properties of statistical inferences in the context of finite populations are harder to determine than in the iid case due to their dependence jointly on the characteristics of the finite population and the sampling design employed. There have been many discussions on special inference procedures under special sampling designs in the literature. General and comprehensive results ar...

Two-phase sampling design is a common practice in many medical studies with rare disorders. Generally the first-phase classification is fallible but relatively cheap, while the accurate second-phase state of-the-art medical diagnosis is complex and rather expensive to perform. When constructed efficiently it offers great potential for higher true case detection as well as for higher precision. ...

The bootstrap method is often used for variance estimation in sample surveys with a stratified multistage sampling design. It typically implemented by producing set of weights that made available to users and accounts the complexity Rao–Wu–Yue produce required weights. valid under with-replacement at first stage or fixed-size without-replacement provided first-stage fractions are negligible. So...

This paper deals with the problem of estimation of population mean in two-phase sampling. A ratio-product estimator of population mean using known coefficient of kurtosis of two auxiliary variates has been proposed. In fact, it is a two-phase sampling version of Tailor et al. (2010) estimator and its properties are studied. Proposed estimator has been compared with usual unbiased estimator, cla...