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Unequal Probability Sampling Strategies with Application to Adolescent Health Studies

Wang, Jianmin. (2001). Unequal Probability Sampling Strategies with Application to Adolescent Health Studies. Master's thesis / Doctoral dissertation, The University of North Carolina at Chapel Hill.

Wang, Jianmin. (2001). Unequal Probability Sampling Strategies with Application to Adolescent Health Studies. Master's thesis / Doctoral dissertation, The University of North Carolina at Chapel Hill.

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The National Longitudinal Study of Adolescent Health is a study of the health related behavior of adolescents in high school in the United States where high schools were first selected without replacement from a primary sampling frame with varying probabilities of selection. The goal is to estimate several health related parameters. To estimate the finite population parameters using the data from sample, the Horvitz-Thompson estimator is a choice for population total. Asymptotic bias and normality of Horvitz-Thompson estimator and variance-covariance estimate of Horvitz-Thompson estimator for non-linear function of population totals are studied. We develop, through coupon collecter's problem, sufficient conditions under which in the multivariate case the Horvitz-Thompson estimator is asymptoticlly multinormal under the sampling scheme of successive sampling with varying probabilities without replacement (SSVPWOR). An approximate Horvitz-Thompson estimator (AHTE) is proposed based on the approximation of the first order inclusion probabilities. This theory is applicable when SSVPWOR is used in a one-stage sampling survey and when SSVPWOR is used in the first stage of the sampling within a multi-stage sampling survey. The method of estimating the variance-covariance matrix is derived for the one-stage SSVPWOR and for the multi-stage sampling survey with the SSVPWOR method in the first stage. A modified jackknife method is developed for SSVPWOR successfully. The consistency of the modified jackknife variance estimator is established. To verify the applicability of these methods, simulation experiments were conducted on real population data. The results indicate that the ANTE and its variance-covariance matrix estimate are consistent. The multivariate normality of the ANTE is mainly influenced by the weighted frequency of the ratio of study variables to the selection probabilities. Increase of the population size and sample size can improve the normality of the AHTE. The sampling fraction at the second stage of two-stage sampling has no effect on the normality of the AHTE. The data form the National Longitudinal Study of Adolescent Health are analyzed by the developed methods to estimate the non linear functions of population totals, such as proportion of public high schools with sex education program in 10th grade.




THES



Wang, Jianmin


Sen, Pranab K. Suchindran Chirayath M.

2001



3031926


152-152 p.




The University of North Carolina at Chapel Hill

Ann Arbor

9780493446394; 0493446397




1995