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 Title: Effect size estimation and robust classification for irregularly sampled functional data Author(s): Park, Yeon Joo Director of Research: Simpson, Douglas G Doctoral Committee Chair(s): Simpson, Douglas G Doctoral Committee Member(s): Douglas, Jeffrey A; Liang, Feng; Shao, Xiaofeng Department / Program: Statistics Discipline: Statistics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Effect size Functional ANOVA Functional central limit theorem Functional random effect model Irregular functional data Power analysis Probabilistic classification Quantitative image analysis Robustness Signal-to-noise ratio Abstract: Functional data arise frequently in numerous scientific fields with the development of modern technology. Accordingly, functional data analysis to extract information on curves or functions is an important area for investigation. In this thesis, we address two key issues: measuring an effect size of variable of the interest in functional analysis of variance (fANOVA) model and the development of robust probabilistic classifier in functional response model. We especially consider irregular functional data in our study, where curves are collected over varying or non-overlapping intervals. First, we develop an approach to quantify the effect size on functional data, perform functional ANOVA hypothesis test, and conduct power analysis. We develop an approach to quantify the effect size on functional data, perform functional ANOVA hypothesis test, and conduct power analysis. We introduce the functional signal-to-noise ratio ($fSNR$), visualize the magnitude of effects over the interval of interest, and perform bootstrapped inferences. It can be applicable when the individual curves are sampled at irregularly spaced points or collected over varying intervals. The proposed methods are applied in the analysis of functional data from inter-laboratory quantitative ultrasound measurements, and in a reanalysis of Canadian weather data. Moreover, we represent the asymptotic power of functional ANOVA test as a function of proposed measure. The agreement between the asymptotic and empirical results is examined and found to be quite good even for small sample sizes. The asymptotic lower bound of power can be reasonably used to determine sample size in planning experimental design. Second, we build a robust probabilistic classifier for functional data, which predicts the membership for given input as well as provides informative posterior probability distribution over a set of classes. This method combines Bayes formula and semiparametric mixed effects model with robust tuning parameter. We aim to make the method robust to outlying curves especially in providing robust degree of certainty in prediction, which is crucial in medical diagnosis. It can be applicable to various practical structures, such as unequally and sparsely collected samples or repeatedly measured curves retaining between-curve correlation, with very flexible spatial covariance function. As an illustration we conduct simulation studies to investigate the sensitivity behaviors of probability estimates to outlying curves under Gaussian assumption and compare our proposed classifier with other functional classification approaches. The performance is evaluated by imposing more penalty for being confident but false prediction. The value of the proposed approach hinges on its simple, flexible, and computational efficiency. We illustrate the issues and methodology in ultrasound quantitative ultrasound, backscatter coefficient vs. frequency functional data, commonly obtained as irregular form and public dataset with artificial contamination. We also show how to implement proposed classifier in R. Issue Date: 2017-07-10 Type: Thesis URI: http://hdl.handle.net/2142/98126 Rights Information: Copyright 2017 Yeonjoo Park Date Available in IDEALS: 2017-09-29 Date Deposited: 2017-08
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