STATISTICAL INFERENCE IN FINITE POPULATION SAMPLING WHEN AUXILIARY INFORMATION IS AVAILABLE

摘要

The ratio estimator can be justified by a linear superpopulation model without intercept and the error variance proportional to the size of the covariate. If either assumption is violated, other estimators may be preferred. In Chapter 2 we consider a class of estimators which are based on different assumptions about the error variance structure. Some finite population decompositions are introduced to study the design-consistency of estimators under consideration. For p auxiliary variables, we characterize the class of consistent weighted least squares estimators. This characterization is extended to the infinite population problem.;In Chapter 3 we compare the efficiency of a class of weighted regression estimators including the multivariate regression estimator. We prove that under simple random sampling the unweighted regression estimator is the most efficient one.;In Chapter 4 we consider the leading terms of the biases of the ratio and regression estimators. By fitting a regression line to y and x in the finite population, we show that the intercept of the regression line causes the leading term of the bias. A different decomposition is used for the regression estimator. By fitting a quadratic regression to the population, we show that the leading term of the bias is caused by the quadratic term. We also give a compact and intuitive formula for the leading term of the bias of the p dimensional weighted regression estimators.;Finally, in Chapter 5 we study the variance estimation problem for the linear regression estimator. We propose a new class of estimators of variance of the regression estimator in analogy of Wu's (1982a) work for the ratio. The optimal variance estimator within the class is found. We also consider several different variance estimators proposed in the literature. We prove that the jackknife variance estimator asymptotically overestimates the mean square error of the regression estimator. An empirical study is given to compare the performance of these variance estimators. Three criteria are used: mean square error and bias of the variance estimator and coverage probability of the associated confidence interval.