Kennel, TimothyThis dissertation describes three distinct research papers. Although each research topic is different and there is very little binding some of the chapters together, all three deal with innovations to model-assisted estimators. Moreover, all three papers explore different aspects of estimating totals, means, and rates from clustered samples. New estimators are presented. Their theoretical properties are explored; and, simulations are used to explore their design-based properties in realistic situations. After an introductory chapter, we show how leverage adjustments can be made to sandwich variance estimators to improve variance estimates of Generalized Regression estimators in two-staged samples. In the third chapter, we explore multinomial logistic-assisted estimators of finite population totals in clustered samples. In the final chapter, we use generalized linear models to assist estimating finite population totals in cluster samples.DissertationStatisticsClustered SampleLeverageModel-Assisted EstimationMultinomialSurvey StatisticsVariance