Browsing by Author "Iyer, Hariharan K., advisor"

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Open Access
A fiducial approach to extremes and multiple comparisons
(Colorado State University. Libraries, 2010) Wandler, Damian V., author; Hannig, Jan, advisor; Iyer, Hariharan K., advisor; Chong, Edwin Kah Pin, committee member; Wang, Haonan, committee member
Generalized fiducial inference is a powerful tool for many difficult problems. Based on an extension of R. A. Fisher's work, we used generalized fiducial inference for two extreme value problems and a multiple comparison procedure. The first extreme value problem is dealing with the generalized Pareto distribution. The generalized Pareto distribution is relevant to many situations when modeling extremes of random variables. We use a fiducial framework to perform inference on the parameters and the extreme quantiles of the generalized Pareto. This inference technique is demonstrated in both cases when the threshold is a known and unknown parameter. Simulation results suggest good empirical properties and compared favorably to similar Bayesian and frequentist methods. The second extreme value problem pertains to the largest mean of a multivariate normal distribution. Difficulties arise when two or more of the means are simultaneously the largest mean. Our solution uses a generalized fiducial distribution and allows for equal largest means to alleviate the overestimation that commonly occurs. Theoretical calculations, simulation results, and application suggest our solution possesses promising asymptotic and empirical properties. Our solution to the largest mean problem arose from our ability to identify the correct largest mean(s). This essentially became a model selection problem. As a result, we applied a similar model selection approach to the multiple comparison problem. We allowed for all possible groupings (of equality) of the means of k independent normal distributions. Our resulting fiducial probability for the groupings of the means demonstrates the effectiveness of our method by selecting the correct grouping at a high rate.
Open Access
Applications of generalized fiducial inference
(Colorado State University. Libraries, 2009) E, Lidong, author; Iyer, Hariharan K., advisor
Hannig (2008) generalized Fisher's fiducial argument and obtained a fiducial recipe for interval estimation that is applicable in virtually any situation. In this dissertation research, we apply this fiducial recipe and fiducial generalized pivotal quantity to make inference in four practical problems. The list of problems we consider is (a) confidence intervals for variance components in an unbalanced two-component normal mixed linear model; (b) confidence intervals for median lethal dose (LD50) in bioassay experiments; (c) confidence intervals for the concordance correlation coefficient (CCC) in method comparison; (d) simultaneous confidence intervals for ratios of means of Lognormal distributions. For all the fiducial generalized confidence intervals (a)-(d), we conducted a simulation study to evaluate their performance and compare them with other competing confidence interval procedures from the literature. We also proved that the intervals (a) and (d) have asymptotically exact frequentist coverage.
Open Access
Data mining techniques for temporal point processes applied to insurance claims data
(Colorado State University. Libraries, 2008) Iverson, Todd Ashley, author; Ben-Hur, Asa, advisor; Iyer, Hariharan K., advisor
We explore data mining on databases consisting of insurance claims information. This dissertation focuses on two major topics we considered by way of data mining procedures. One is the development of a classification rule using kernels and support vector machines. The other is the discovery of association rules using the Apriori algorithm, its extensions, as well as a new association rules technique. With regard to the first topic we address the question-can kernel methods using an SVM classifier be used to predict patients at risk of type 2 diabetes using three years of insurance claims data? We report the results of a study in which we tested the performance of new methods for data extracted from the MarketScan® database. We summarize the results of applying popular kernels, as well as new kernels constructed specifically for this task, for support vector machines on data derived from this database. We were able to predict patients at risk of type 2 diabetes with nearly 80% success when combining a number of specialized kernels. The specific form of the data, that of a timed sequence, led us to develop two new kernels inspired by dynamic time warping. The Global Time Warping (GTW) and Local Time Warping (LTW) kernels build on an existing time warping kernel by including the timing coefficients present in classical time warping, while providing a solution for the diagonal dominance present in most alignment methods. We show that the LTW kernel performs significantly better than the existing time warping kernel when the times contained relevant information. With regard to the second topic, we provide a new theorem on closed rules that could help substantially improve the time to find a specific type of rule. An insurance claims database contains codes indicating associated diagnoses and the resulting procedures for each claim. The rules that we consider are of the form diagnoses imply procedures. In addition, we introduce a new class of interesting association rules in the context of medical claims databases and illustrate their potential uses by extracting example rules from the MarketScan® database.
Open Access
Model selection based on expected squared Hellinger distance
(Colorado State University. Libraries, 2007) Cao, Xiaofan, author; Iyer, Hariharan K., advisor; Wang, Haonan, advisor
This dissertation is motivated by a general model selection problem such that the true model is unknown and one or more approximating parametric families of models are given along with strategies for estimating the parameters using data. We develop model selection methods based on Hellinger distance that can be applied to a wide range of modeling problems without posing the typical assumptions for the true model to be within the approximating families or to come from a particular parametric family. We propose two estimators for the expected squared Hellinger distance as the model selection criteria.