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Non-Parametric and Semi-Parametric Estimation and Inference with Applications to Finance and Bioinformatics

In this dissertation, we develop tools from non-parametric and semi-parametric statistics to perform estimation and inference. In the first chapter, we propose a new method called Non-Parametric Outlier Identification and Smoothing (NOIS), which robustly smooths stock prices, automatically detects outliers and constructs pointwise confidence bands around the resulting curves. In real- world examples of high-frequency data, NOIS successfully detects erroneous prices as outliers and uncovers borderline cases for further study. NOIS can also highlight notable features and reveal new insights in inter-day chart patterns. In the second chapter, we focus on a method for non-parametric inference called empirical likelihood (EL). Computation of EL in the case of a fixed parameter vector is a convex optimization problem easily solved by Lagrange multipliers. In the case of a composite empirical likelihood (CEL) test where certain components of the parameter vector are free to vary, the optimization problem becomes non-convex and much more difficult. We propose a new algorithm for the CEL problem named the BI-Linear Algorithm for Composite EmPirical Likelihood (BICEP). We extend the BICEP framework by introducing a new method called Robust Empirical Likelihood (REL) that detects outliers and greatly improves the inference in comparison to the non-robust EL. The REL method is combined with CEL by the TRI-Linear Algorithm for Composite EmPirical Likelihood (TRICEP). We demonstrate the efficacy of the proposed methods on simulated and real world datasets. We present a novel semi-parametric method for variable selection with interesting biological applications in the final chapter. In bioinformatics datasets the experimental units often have structured relationships that are non-linear and hierarchical. For example, in microbiome data the individual taxonomic units are connected to each other through a phylogenetic tree. Conventional techniques for selecting relevant taxa either do not account for the pairwise dependencies between taxa, or assume linear relationships. In this work we propose a new framework for variable selection called Semi-Parametric Affinity Based Selection (SPAS), which has the flexibility to utilize struc- tured and non-parametric relationships between variables. In synthetic data experiments SPAS outperforms existing methods and on real world microbiome datasets it selects taxa according to their phylogenetic similarities. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / April 19, 2018. / Bioinformatics, Empirical likelihood, Finance, Non-parametric, Outlier detection, Variable selection / Includes bibliographical references. / Yiyuan She, Professor Directing Dissertation; Giray Okten, University Representative; Eric Chicken, Committee Member; Xufeng Niu, Committee Member; Minjing Tao, Committee Member.

Identiferoai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_653516
ContributorsTran, Hoang Trong (author), She, Yiyuan (professor directing dissertation), Ökten, Giray (university representative), Chicken, Eric, 1963- (committee member), Niu, Xufeng, 1954- (committee member), Tao, Minjing (committee member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg)
PublisherFlorida State University
Source SetsFlorida State University
LanguageEnglish, English
Detected LanguageEnglish
TypeText, text, doctoral thesis
Format1 online resource (125 pages), computer, application/pdf

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