The two-phase sample design is often employed in sample surveys for various reasons. It has a long history, first introduced by Neyman (1938). Traditionally, the technique is used to collect some auxiliary data that are not available for the sampling frame from a large first-phase sample to use the data at the second-phase sampling. The technique, sometimes called “double sampling” has many app...

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch and Wild (...

Two-phase sampling is often used in a wide variety of surveys. Variance estimation from a two-phase sample has been a subject of active research. The re-sampling method of variance estimation has been used for this problem. However, the method confronts a challenging problem when the first phase sampling fraction is high. In the extreme (but not uncommon) case some first-phase strata are take-a...

The problem of variance estimation in two phase sampling under non response was not considered in the literature. We have adapted the classes of variance estimators suggested by Srivastava and Jhajj (1980) into the two phase sampling under the strategy given by Hansen and Hurwitz (1946) for the problem of non-response. In this paper some more generalize classes of estimators for the population ...

We consider estimation of the causal effect of a treatment on an outcome from observational data collected in two phases. In the first phase, a simple random sample of individuals is drawn from a population. On these individuals, information is obtained on treatment, outcome and a few low dimensional covariates. These individuals are then stratified according to these factors. In the second pha...

This paper considers the problem of estimating the population mean Y of the study variate y with two auxiliary variates x and z in the presence of non-response using twophase (double) sampling procedure. Four classes of combined regression and ratio estimators have been defined in four different situations and their properties are studied under large sample approximation. Comparisons of the sug...

To estimate the population mean with imputation, i.e. the technique of substituting missing data, there are a number of techniques available in literature like Ratio method of imputation, Compromised method of imputation, Mean method of imputation, Ahmed’s methods of imputation, F-T methods of imputation and so on. If population mean of auxiliary information is unknown then these methods are no...

The answer to this question lies in knowing the moral standing of Phase IV studies and whether we ought to conduct them. And to know this, in part, we need to compare them to studies in Phases I, II, and III and then determine where Phase IV studies stand in relation to Phase I–III studies scientifically and commercially.

We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is wellposed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exists at certain times. We prove that the model problem has a smooth soluti...

This work describes a prototype-based online handwritten character recognition system and a two-phase recognition scheme aimed to speed up the recognition. In the first phase, the prototype set is pruned and ordered on the basis of preclassification performed with heavily down-sampled characters and prototypes. In the second phase, the final classification is performed without down-sampling by ...