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The main focus of many agricultural, ecological and environmental studies is to develop well designed, cost-effective and efficient sampling designs. Ranked set sampling (RSS) is one of those sampling methods that can help accomplish such objectives by incorporating prior information and expert knowledge to the design. In this thesis, new RSS schemes are suggested for efficiently estimating the population mean. These sampling schemes can be used as cost-effective alternatives to the traditional simple random sampling (SRS) and RSS schemes. It is shown that the mean estimators under the proposed sampling schemes are at least as efficient as the mean estimator with SRS. We consider the best linear unbiased estimators (BLUEs) and the best linear invariant estimators (BLIEs) for the unknown parameters (location and scale) of a location-scale family of distributions under double RSS (DRSS) scheme. The BLUEs and BLIEs with DRSS are more precise than their counterparts based on SRS and RSS schemes. We also consider the BLUEs based on DRSS and ordered DRSS (ODRSS) schemes for the unknown parameters of a simple linear regression model using replicated observations. It turns out that, in terms of relative efficiencies, the BLUEs under ODRSS are better than the BLUEs with SRS, RSS, ordered RSS (ORSS) and DRSS schemes. Quality control charts are widely recognized for their potential to be a powerful process monitoring tool of the statistical process control. These control charts are frequently used in many industrial and service organizations to monitor in-control and out-of-control performances of a production or manufacturing process. The RSS schemes have had considerable attention in the construction of quality control charts. We propose new exponentially weighted moving average (EWMA) control charts for monitoring the process mean and the process dispersion based on the BLUEs obtained under ORSS and ODRSS schemes. We also suggest an improved maximum EWMA control chart for simultaneously monitoring the process mean and dispersion based on the BLUEs with ORSS scheme. The proposed EWMA control charts perform substantially better than their counterparts based on SRS and RSS schemes. Finally, some new EWMA charts are also suggested for monitoring the process dispersion using the best linear unbiased absolute estimators of the scale parameter under SRS and RSS schemes.

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In this dissertation, we explore and illustrate the concept of ranked sparsity, a phenomenon that often occurs naturally in the presence of derived variables. Ranked sparsity arises in modeling applications when an expected disparity exists in the quality of information between different feature sets. Its presence can cause traditional model selection methods to fail because statisticians commonly presume that each potential parameter is equally worthy of entering into the final model - we call this principle "covariate equipoise". However, this presumption does not always hold, especially in the presence of derived variables. For instance, when all possible interactions are considered as candidate predictors, the presumption of covariate equipoise will often produce misclassified and opaque models. The sheer number of additional candidate variables grossly inflates the number of false discoveries in the interactions, resulting in unnecessarily complex and difficult-to-interpret models with many (truly spurious) interactions. We suggest a modeling strategy that requires a stronger level of evidence in order to allow certain variables (e.g. interactions) to be selected in the final model. This ranked sparsity paradigm can be implemented either with a modified Bayesian information criterion (RBIC) or with the sparsity-ranked lasso (SRL). In chapter 1, we provide a philosophical motivation for ranked sparsity by describing situations where traditional model selection methods fail. Chapter 1 also presents some of the relevant literature, and motivates why ranked sparsity methods are necessary in the context of interactions. Finally, we introduce RBIC and SRL as possible recourses. In chapter 2, we explore the performance of SRL relative to competing methods for selecting polynomials and interactions in a series of simulations. We show that the SRL is a very attractive method because it is fast, accurate, and does not tend to inflate the number of Type I errors in the interactions. We illustrate its utility in an application to predict the survival of lung cancer patients using a set of gene expression measurements and clinical covariates, searching in particular for gene-environment interactions, which are very difficult to find in practice. In chapter 3, we present three extensions of the SRL in very different contexts. First, we show how the method can be used to optimize for cost and prediction accuracy simulataneously when covariates have differing collection costs. In this setting, the SRL produces what we call "minimally invasive" models, i.e. models that can easily (and cheaply) be applied to new data. Second, we investigate the use of the SRL in the context of time series regression, where we evaluate our method against several other state-of-the-art techniques in predicting the hourly number of arrivals at the Emergency Department of the University of Iowa Hospitals and Clinics. Finally, we show how the SRL can be utilized to balance model stability and model adaptivity in an application which uses a rich new source of smartphone thermometer data to predict flu incidence in real time.

As dissatisfaction with the single member district has grown in recent years, new electoral systems have gained popularity. In particular, the Top Four Primary plus Ranked Choice Voting system, enacted in 2020 and used in Alaska for the first time in 2022, has received considerable attention. Besides reducing partisanship, the system claims to increase voter turnout and encourage third-party candidates and candidates of color to run on election day. Given its novelty, however, a comprehensive overview of the system and the implementation process is currently lacking. As a result, the purpose of this study is to assess the history, passage, challenges, and current debate around the Top Four Primary plus Ranked Choice Voting system. Using popular opinion data, candidate campaign techniques, archives, and ballot data, I find that voter and candidate reactions to the system varied, that incumbent advantage was not evident in the 2022 election cycle, and that voting patterns were associated with campaign strategies. States considering the Top Four Primary plus Ranked Choice Voting system can use this thesis as a guide to understanding the system's successes and drawbacks better. The study could also serve as a starting point for researchers looking into how the Top Four Primary plus Ranked Choice Voting system can enhance democracy.

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