Statistical Inference of Ratio Estimation under Adaptive Cluster Sampling

• Main Authors: Feng-MinLin, 林楓敏
• Other Authors: Chang-Tai Chao
• Format: Others
• Language: en_US
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/24509336825530128551

博士 === 國立成功大學 === 統計學系 === 102 === Adaptive cluster sampling is able to provide more efficient estimators of the population quantity of interest together with more abundant sampling yields compared to the conventional sampling designs when the population is a rare and clustered one. Various adaptive sampling designs with respect to different initial conventional designs have been developed in the past, and they have been applied in different disciplines, such as environmental research, ecological research, sociology, and epidemiology studies. Originally, the unbiased estimators in adaptive cluster sampling are not the functions of the minimal sufficient statistic, and certain information obtained from the sample is not utilized in the estimators. For better estimation results, different Rao-Blackwellized unbiased estimators based on the minimal sufficient statistic and certain sufficient statistic also have been proposed in the past, and successfully provided better estimation results. Often certain auxiliary variables would also be available in a sampling survey situation, and one would like to utilize this auxiliary information into the estimation so that he can take advantage of the correlation between the primary and auxiliary variables. Ratio estimators which make use of the original unbiased estimators have been proposed, and they are able to provide better estimation results when the primary and auxiliary variables are related in a certain degree. In addition, improved ratio estimators based on the univariate Rao-Blackwellized estimators are also proposed in past researches, and they can effectively outperform the original ratio estimators. Nevertheless, the variances and variance estimators of the improved ratio estimators are still unavailable, hence it is of both practical and theoretical interest to investigate the related issue in order to establish a complete inference. In this article, the variances and the associated variance estimators of these improved ratio estimators are proposed for a thorough framework of statistical inference under adaptive cluster sampling. Performance of the proposed variance estimators is evaluated in terms of the absolute relative percentage bias and the empirical mean-squared error. As expected, results show that both the absolute relative percentage bias and the empirical mean-squared error decrease as the initial sample size increases for all the variance estimators. To evaluate the confidence intervals based on these variance estimators and the finite population Central Limit Theorem, the coverage rate and the interval width are employed. These confidence intervals suffer similar disadvantage as that of the conventional ratio estimator. Hence, alternative confidence intervals based on a certain type of adjusted variance estimators are constructed and assessed in this article. Additionally, the population in which adaptive cluster sampling would be an appropriate sampling design is often highly skewed, hence the CLT-based confidence interval often fails to provide appropriate coverage probability. Hence, it is of interest to further study on the feasibility of non-parametric type of confidence intervals based on the effective usage of auxiliary information. In the second part of this article, we propose two types of pseudo-empirical likelihood ratio confidence intervals based on the usage of auxiliary information and compare the performance of the pseudo-empirical based confidence intervals with the CLT-based confidence intervals based on the ratio estimators using a simulation study. The simulation results show that the confidence intervals obtained from both types of pseudo-empirical likelihood methods perform slightly better.