Some contributions to small area estimation

This dissertation consists of nine chapters. Chapter 1 is an introduction to small area estimation. It presents a review of small area problem and related estimation approaches including empirical best linear unbiased prediction (EBLUP) approach and Bayes approach. EBLUP approach includes EBLUP estimators and mean squared error (MSE) approximation. Bayes approach includes empirical Bayes (EB) analysis and MSE approximation by using the jackknife method. Chapters 2 to 8 contain several developments in the topic of small area estimation. Chapter 9 gives some topics for future research.; In Chapter 2, a new generalized regression (GREG) estimator of a small area mean under a two-level model is studied. We derive the MSE of the new GREG estimator under the model and compare it to the MSE of the BLUP estimator. We also provide empirical results on the relative efficiency of the estimators when the model parameters are estimated.; In Chapter 3, we derive a second order approximation to the MSE of the pseudo-EBLUP estimator, introduced by You and Rao (2002), of a small area mean. Using this approximation, an estimator of MSE that is approximately unbiased is derived. Empirical results on the performance of the proposed approximation are also presented.; In Chapter 4, a sub-area level small area model is introduced. Not only may this model be used to estimate small area means by borrowing strength from related area levels, but also it can borrow strength from sub-area levels to obtain more efficient sub-area estimators. We obtain second order approximations to the MSE of the model-based small area estimators and then derive MSE estimators unbiased to second order. Results of a simulation study on the accuracy of the second order approximation to the MSE and the bias of the estimators of the MSE are also reported.; In Chapter 5, a conditional MSE estimation for the nested error linear regression model is studied. We derive a second order approximation to the conditional MSE given the area-specific response data. We then derive a nearly unbiased estimator of the conditional MSE. A data analysis on the performance of our approach is also provided.; In Chapter 6, we derive second order approximations of the MSE and the conditional MSE given yi = (yi 1, ..., yini )' of m&d4;iw under the nested error linear regression model. Moreover, we derive the estimators of MSE and conditional MSE of m&d4;iw that are nearly unbiased.; In Chapter 7, a structural measurement error model with unit-specific covariates xij in the nested error regression model is studied. We study the asymptotic behavior of Bayes risk of EB estimators, along the lines of Ghosh and Sinha (2006), and establish asymptotic optimality of EB estimators. Moreover, we find a second order approximation to the MSE of EB estimators and obtain a MSE estimator which is nearly unbiased. A simulation study on the performance of the proposed method is also provided.; In Chapter 8, we study the functional measurement error nested error regression model with unit level covariates xij. We study the asymptotic behavior of Bayes risk of pseudo-EB (PEB) estimators and establish the asymptotic optimality of the pseudo-EB estimators. Moreover, we find a second order approximation to the MSE of PEB estimators and obtain a MSE estimator which is nearly unbiased. Empirical results on the performance of the proposed pseudo-EB estimators are also presented.; Finally, some suggestions for future research are presented in Chapter 9.