Thesis (Ph. D.)--University of Washington, 2006. / Vita. Includes bibliographical references (p. 257-261).

Thesis (Ph. D.)--University of Rhode Island, 2006. / Includes bibliographical references (leaves 99-100).

Master of Science / Department of Statistics / Perla E. Reyes Cuellar / The term network has become part of our everyday vocabulary. The more popular are perhaps the social ones, but the concept also includes business partnerships, literature citations, biological networks, among others. Formally, networks are defined as sets of items and their connections. Often modeled as the mathematic object known as a graph, networks have been studied extensively for several years, and research is widely available. In statistics, a variety of modeling techniques and statistical terms have been developed to analyze them and predict individual behaviors. Specifically, certain statistics like degree distribution, clustering coefficient, and so on are considered important indicators in traditional social network studies. However, while conventional network models assume that the whole network population is known, complete information is not always available. Thus, different sampling methods are often required when the population data is inaccessible. Less time has been dedicated to studying the accuracy of these sampling methods to produce a representative sample. As such, the aim of this report is to identify the capacity of sampling techniques to reflect the features of the original network. In particular, we study Anti-cluster Respondent Driven Sampling (AC-RDS). We also explore whether standard modeling techniques paired with sample data could estimate statistics often used in the study of social networks. Respondent Driven Sampling (RDS) is a chain referral approach to study rare and/or hidden populations. Originating from the link-tracing design, RDS has been further developed into a series of methods utilized in social network studies, such as locating target populations or estimating the number and proportion of needle-sharing among drug addicts. However, RDS does not always perform as well as expected. When the social network contains tight communities (or clusters) with few connections between them, traditional RDS tends to oversample one community, introducing bias. AC-RDS is a special Markov chain process that collects samples across communities, capturing the whole network. With special referral requests, the initial seeds are more likely to refer to the individuals that are outside their communities. In this report, we fitted the Exponential Random Graph Model (ERGM) and a Stochastic Block Model (SBM) to an empirical study of the Facebook friendship network of 1034 participants. Then, given our goal of identifying techniques that will produce a representative sample, we decided to compare two version of AC-RDSs, in addition to traditional RDS, with Simple Random Sampling (SRS). We compared the methods by drawing 100 network samples using each sampling technique, then fitting an SBM to each sample network we used the results to project the network into one of population size. We calculated essential network statistics, such as degree distribution, of each sampling method and then compared the result to the original network observed statistics.

Doctor of Philosophy / Department of Agricultural Economics / Allen M. Featherstone / This dissertation focuses on measuring the efficiency and productivity for agricultural cooperatives in the United States using the data envelopment analysis (DEA) approach. Economic measures such as cost efficiency, economies of scale, and economies of scope are measured by estimating a cost frontier in a multiproduct framework. Productivity growth is measured using the biennial Malmquist index approach. The cost frontier is the basis for calculating cost efficiency, economies of scale, and economies of scope as the cost frontier estimation in a multiproduct approach describes how cost changes as output changes. The estimates of economies of scale and scope have important implications for agricultural cooperatives because most of the cooperatives sell more than one product. Understanding the impact of changing output levels or mixes on the cost structure is helpful to improve the performance of cooperatives. Further, scope economies estimate the percentage of cost savings through product diversification in a multiproduct firm. The trade-off between cost efficiency and multiproduct scale economies allows the estimation of whether a higher percentage of cost can be eliminated by becoming cost efficient or changing the scale of operations. The economic measures are estimated using a single cost frontier (multi-year frontier) and annual cost frontiers. Multiproduct economies of scale and economies of scope exist indicating that increasing scale and product diversification can reduce cost for agricultural cooperatives. The mean values of product-specific economies of scale for all outputs are close to one indicating that cooperatives are operating close to constant returns to scale. The comparison between cost efficiency and scale economies suggests that smaller cooperatives can save a higher percentage of cost by increasing the scale of operations rather than just becoming cost efficient. Because larger incentives exist for small cooperatives to increase scale, mergers will likely continue until economies of scale are exhausted in the industry. Annual estimates show that agricultural cooperatives have become less cost efficient over time, but economies of scale and economies of scope remain consistent across years. Many agricultural cooperatives face economies of scale indicating that variable returns to scale as opposed to constant returns to scale is the appropriate technology for modeling agricultural farm marketing and supply cooperatives. Further, the Kolmogorov-Smirnov (KS) test and two sample t-test are used to examine whether economic measures estimated from a single frontier and annual frontiers are statistically different. The KS test and t-test indicate that economic measures obtained from the single frontier are statistically different from those measures calculated from annual frontiers. This indicates that the cost frontier has shifted over time. Productivity growth of agricultural cooperatives is estimated using the biennial Malmquist productivity index (BMI) under variable returns to scale over the period 2005 to 2014. The BMI avoids numerical infeasibilities under variable returns to scale compared to traditional methods. The BMI is decomposed into efficiency change and technical change to evaluate the sources of productivity growth. Overall, agricultural cooperatives gained 34% cumulative productivity growth during the decade allocated by -2% and 37% cumulative technical efficiency change and technical change over the study period. Technical change was the major source of productivity growth rather than efficiency change. Cooperatives can achieve higher productivity by increasing managerial efficiency and by investing in technology.

Scene parsing, or segmenting all the objects in an image and identifying their categories, is one of the core problems of computer vision. In order to achieve an object-level semantic segmentation, we build upon the recent superparsing approach by Tighe and Lazebnik, which is a nonparametric solution to the image labeling problem. Superparsing consists of four steps. For a new query image, the most similar images from the training dataset of labeled images is retrieved based on global features. In the second step, the query image is segmented into superpxiels and 20 di erent local features are computed for each superpixel. We propose to use the SLICO segmentation method to allow control of the size, shape and compactness of the superpixels because SLICO is able to produce accurate boundaries. After all superpixel features have been extracted, feature-based matching of superpixels is performed to nd the nearest-neighbour superpixels in the retrieval set for each query superpxiel. Based on the neighbouring superpixels a likelihood score for each class is calculated. Finally, we formulate a Conditional Random Field (CRF) using the likelihoods and a pairwise cost both computed from nonparametric estimation to optimize the labeling of the image. Speci cally, we de ne a novel pairwise cost to provide stronger semantic contextual constraints by incorporating the similarity of adjacent superpixels depending on local features. The optimized labeling obtained with the CRF results in superpixels with the same labels grouped together to generate segmentation results which also identify the categories of objects in an image. We evaluate our improvements to the superparsing approach using segmentation evaluation measures as well as the per-pixel rate and average per-class rate in a labeling evaluation. We demonstrate the success of our modi ed approach on the SIFT Flow dataset, and compare our results with the basic superparsing methods proposed by Tighe and Lazebnik.

The Dirichlet process is perhaps the most popular prior used in the nonparametric Bayesian inference. This prior which is placed on the space of probability distributions has conjugacy property and asymptotic consistency. In this thesis, our concentration is on applying this nonparametric Bayesian inference on the Tukey depth and Tukey median. Due to the complexity of the distribution of Tukey median, we use this nonparametric Bayesian inference, namely the Lo’s bootstrap, to approximate the distribution of the Tukey median. We also compare our results with the Efron’s bootstrap and Rubin’s bootstrap. Furthermore, the existing asymptotic theory for the Tukey median is reviewed. Based on these existing results, we conjecture that the bootstrap sample Tukey median converges to the same asymp- totic distribution and our simulation supports the conjecture that the asymptotic consistency holds.

From the airport security guard monitoring luggage to the rushed commuter looking for their car keys, visual search is one of the most common requirements of our visual system. Despite its ubiquity, many aspects of visual search remain unaccounted for by computational models. Difficulty arises when trying to account for any internal biases of an observer undertaking a search task or trying to decompose an image of a natural scene into relevant fundamental properties. Previous studies have attempted to understand visual search by using highly simplified stimuli, such as discrete search arrays. Although these studies have been useful, the extent to which the search of discrete search arrays can represent the search of more naturalistic stimuli is subject to debate. The experiments described in this thesis used as stimuli images of natural scenes and attempted to address two key objectives. The first was to determine which image properties influenced the detectability of a target. Features investigated included chroma, entropy, contrast, edge contrast and luminance. The proportion of variance in detection ability accounted for by each feature was estimated and the features were ranked in order of importance to detection. The second objective was to develop a method for guiding human fixations by modifying image features while observers were engaged in a search task. To this end, images were modified using the image-processing method unsharp masking. To assess the effect of the image modification on fixations, eye movements were monitored using an eye-tracker. Another subject addressed in the thesis was the classification of fixations from eye movement data. There exists no standard method for achieving this classification. Existing methods have employed thresholds for speed, acceleration, duration and stability of point-of-gaze to classify fixations, but these thresholds have no commonly accepted values. Presented in this thesis is an automatic nonparametric method for classifying fixations, which extracts fixations without requiring any input parameters from the experimenter. The method was tested against independent classifications by three experts. The accurate estimation of Kullback-Leibler Divergence, an information theoretic quantity which can be used to compare probability distributions, was also addressed in this thesis since the quantity was used to compare fixation distributions. Different methods for the estimation of Kullback-Leibler divergence were tested using artificial data and it was shown than a method for estimating the quantity directly from input data outperformed methods which required binning of data or kernel density estimation to estimate underlying distributions.

Differential item functioning (DIF) can occur across age, gender, ethnic, and/or linguistic groups of examinee populations. Therefore, whenever there is more than one group of examinees involved in a test, a possibility of DIF exists. It is important to detect items with DIF with accurate and powerful statistical methods. While finding a proper DIP method is essential, until now most of the available methods have been dominated by applications to large scale testing contexts. Since the early 1990s, Ramsay has developed a nonparametric item response methodology and computer software, TestGraf (Ramsay, 2000). The nonparametric item response theory (IRT) method requires fewer examinees and items than other item response theory methods and was also designed to detect DIF. However, nonparametric IRT's Type I error rate for DIF detection had not been investigated. The present study investigated the Type I error rate of the nonparametric IRT DIF detection method, when applied to moderate-to-small-scale testing context wherein there were 500 or fewer examinees in a group. In addition, the Mantel-Haenszel (MH) DIF detection method was included. A three-parameter logistic item response model was used to generate data for the two population groups. Each population corresponded to a test of 40 items. Item statistics for the first 34 non-DIF items were randomly chosen from the mathematics test of the 1999 TEVISS (Third International Mathematics and Science Study) for grade eight, whereas item statistics for the last six studied items were adopted from the DIF items used in the study of Muniz, Hambleton, and Xing (2001). These six items were the focus of this study. / Education, Faculty of / Educational and Counselling Psychology, and Special Education (ECPS), Department of / Graduate

Principal surfaces are smooth two-dimensional surfaces that pass through the middle of a p-dimensional data set. They minimise the distance from the data points, and provide a nonlinear summary of the data. The surfaces are nonparametric and their shape is suggested by the data. The formation of a surface is found using an iterative procedure which starts with a linear summary, typically with a principal component plane. Each successive iteration is a local average of the p-dimensional points, where an average is based on a projection of a point onto the nonlinear surface of the previous iteration. Biplots are considered as extensions of the ordinary scatterplot by providing for more than three variables. When the difference between data points are measured using a Euclidean embeddable dissimilarity function, observations and the associated variables can be displayed on a nonlinear biplot. A nonlinear biplot is predictive if information on variables is added in such a way that it allows the values of the variables to be estimated for points in the biplot. Prediction trajectories, which tend to be nonlinear are created on the biplot to allow information about variables to be estimated. The goal is to extend the idea of nonlinear biplot methodology onto principal surfaces. The ultimate emphasis is on high dimensional data where the nonlinear biplot based on a principal surface allows for visualisation of samples, variable trajectories and predictive sets of contour lines. The proposed biplot provides more accurate predictions, with an additional feature of visualising the extent of nonlinearity that exists in the data.

Modeling extreme events is one of the central tasks in risk management and planning, as catastrophes and crises put human lives and financial assets at stake. A common approach to estimate the likelihood of extreme events, using extreme value theory (EVT), studies the asymptotic behavior of the ``tail" portion of data, and suggests suitable parametric distributions to fit the data backed up by their limiting behaviors as the data size or the excess threshold grows. We explore an alternate approach to estimate extreme events that is inspired from recent advances in robust optimization. Our approach represents information about tail behaviors as constraints and attempts to estimate a target extremal quantity of interest (e.g, tail probability above a given high level) by imposing an optimization problem to find a conservative estimate subject to the constraints that encode the tail information capturing belief on the tail distributional shape. We first study programs where the feasible region is restricted to distribution functions with convex tail densities, a feature shared by all common parametric tail distributions. We then extend our work by generalizing the feasible region to distribution functions with monotone derivatives and bounded or infinite moments. In both cases, we study the statistical implications of the resulting optimization problems. Through investigating their optimality structures, we also present how the worst-case tail in general behaves as a linear combination of polynomial decay tails. Numerically, we develop results to reduce these optimization problems into tractable forms that allow solution schemes via linear-programming-based techniques.