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by Yuen Wah-Kong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1980. / Bibliography: leaves 37-38.

by Kwok-leung Tsui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1981. / Bibliography: leaves 39-41.

by Kwok-fai Lee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 85-86). / Chapter CHAPTER 1 --- INTRODUCTION --- p.1 / Chapter §1.1 --- Unequal probabilities sampling schemes without replacement --- p.1 / Chapter §1.2 --- Estimation Problems in unequal probabilities sampling scheme without replacement --- p.3 / Chapter §1.3 --- Classification of unequal probabilities sampling schemes without replacement --- p.5 / Chapter CHAPTER 2 --- ONE-PASS ALGORITHMS --- p.9 / Chapter §2.1 --- Characteristics of one-pass algorithms --- p.9 / Chapter §2.2 --- Existing one-pass algorithms --- p.10 / Chapter §2.2.1 --- Chao's one-pass algorithm / Chapter §2.2.2 --- Other algorithms / Chapter §2.3 --- Second order inclusion probabilities --- p.14 / Chapter CHAPTER 3 --- A NEW ONE-PASS ALGORITHM --- p.17 / Chapter §3.1 --- Introduction --- p.17 / Chapter §3.2 --- Examination of all possible cases --- p.20 / Chapter §3.3 --- Initialization --- p.57 / Chapter §3.4 --- Final step --- p.61 / Chapter §3.5 --- Theorems --- p.64 / Chapter §3.6 --- Worked example --- p.76 / Chapter CHAPTER 4 --- CONCLUSION --- p.83 / References --- p.85

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

Typescript (photocopy). / Digitized by Kansas Correctional Industries

This dissertation is composed of three essays regarding the finite sample properties of estimators for nonparametric models. In the first essay we investigate the finite sample performances of four estimators for additive nonparametric regression models - the backfitting B-estimator, the marginal integration M-estimator and two versions of a two stage 2S-estimator, the first proposed by Kim, Linton and Hengartner (1999) and the second which we propose in this essay. We derive the conditional bias and variance of the 2S estimators and suggest a procedure to obtain optimal bandwidths that minimize an asymptotic approximation of the mean average squared errors (AMASE). We are particularly concerned with the performance of these estimators when bandwidth selection is done based on data driven methods. We compare the estimators' performances based on various bandwidth selection procedures that are currently available in the literature as well as with the procedures proposed herein via a Monte Carlo study. The second essay is concerned with some recently proposed kernel estimators for panel data models. These estimators include the local linear estimator, the quasi-likelihood estimator, the pre-whitening estimators, and the marginal kernel estimator. We focus on the finite sample properties of the above mentioned estimators on random effects panel data models with different within-subject correlation structures. For each estimator, we use the asymptotic mean average squared errors (AMASE) as the criterion function to select the bandwidth. The relative performance of the test estimators are compared based on their average squared errors, average biases and variances. The third essay is concerned with the finite sample properties of estimators for nonparametric regression models with autoregressive errors. The estimators studied are: the local linear, the quasi-likelihood, and two pre-whitening estimators. Bandwidths are selected based on the minimization of the asymptotic mean average squared errors (AMASE) for each estimator. Two regression functions and multiple variants of autoregressive processes are employed in the simulation. Comparison of the relative performances is based mainly on the estimators' average squared errors (ASE). Our ultimate objective is to provide an extensive finite sample comparison among competing estimators with a practically selected bandwidth. / Graduation date: 2006

Post stratification is considered desirable in sample surveys for two reasons - it reduces the mean squared error when averaged over all possible samples, and it reduces the conditional bias when conditioned on stratum sample sizes. The problem studied in this thesis is post stratified estimation of a finite population mean when there is a known auxiliary variable for each population unit. The primary direction of the thesis follows the lines of Holt and Smith (1979). A method is given for using the auxiliary variable in selection of the stratum boundaries and, using this approach to determine strata, to compare post stratified estimates with the self -weighting estimates from the analytical and empirical points of view. Estimates studied are: the post stratified mean, the post stratified combined ratio, and the post stratified separate ratio. The thesis contains simulation results that explore the distributions of the self -weighting estimates, and the post stratified estimates using conditional and unconditional inferences. The correct coverage properties of the confidence intervals are compared and the design effect, i.e. the ratio of the variance of the self -weighting to the variance of post stratified estimates, is calculated from the samples and its distribution explored by the simulation study for several real and artificial populations. The confidence intervals of post stratified estimates using conditional variances had good coverage properties for each sample configuration used, and hence the correct coverage property over all possible samples provided that the Central Limit Theorem was applied. The comparisons indicated that post stratification is an effective approach when the boundaries are obtained based on proper stratification using an auxiliary variable. Moreover it is more efficient than estimation based on simple random sampling in reducing the mean squared error. Finally, there is strong evidence that the post stratified estimates are robust against poorly distributed samples, whereas empirical investigations suggested that the self -weighting estimates are very poor when the samples are unbalanced. / Graduation date: 1990

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Charles W. Therrien, Roberto Cristi. Includes bibliographical references (p. 45). Also available online.