Volatility is usually employed to measure the dispersion of asset returns, and it’s widely used in risk analysis and asset management. This first chapter studies a kernel-based spot volatility matrix estimator with pre-averaging approach for high-frequency data contaminated by market microstructure noise. When the sample size goes to infinity and the bandwidth vanishes, we show that our estimator is consistent and its asymptotic normality is established with achieving an optimal convergence rate. We also construct a consistent pairwise spot co-volatility estimator with Hayashi-Yoshida method for non-synchronous high-frequency data with noise contamination. The simulation studies demonstrate that the proposed estimators work well under different noise levels, and their estimation performances are improved by the increasing sample frequency. In empirical applications, we implement the estimators on the intraday prices of four component stocks of Dow Jones Industrial Average. The second chapter shows a factor-based vast volatility matrix estimation method for high- frequency financial data with market microstructure noise, finite large jumps and infinite activity small jumps. We construct the sample volatility matrix estimator based on the approximate factor model, and use the pre-averaging and thresholding estimation method (PATH) to digest the noise and jumps. After using the principle component analysis (PCA) to decompose the sample volatility matrix estimator, our proposed volatility matrix estimator is finally obtained by imposing the block-diagonal regularization on the residual covariance matrix through sorting the assets with the global industry classification standard (GICS) codes. The Monte Carlo simulation shows that our proposed volatility matrix estimator can remove the majority effects of noise and jumps, and its estimation performance improves fast when the sample frequency increases. Finally, the PCA-based estimators are employed to perform volatility matrix estimation and asset allocation for S&P 500 stocks. To compare with PCA-based estimators, we also include the exchange-traded funds (ETFs) data to construct observable factors such as the Fama-French factors for volatility estimation. / 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 17, 2018. / Factor Model, High-frequency data, Jumps, Market microstructure noise, PCA, Volatility matrix / Includes bibliographical references. / Minjing Tao, Professor Directing Dissertation; Yingmei Cheng, University Representative; Fred Huffer, Committee Member; Xu-Feng Niu, Committee Member.

Statistical tests for biomarker identification and classification methods for patient grouping are two important topics in adaptive designs of clinical trials. In this article, we evaluate four test methods for biomarker identification: a model-based identification method, the popular t-test, the nonparametric Wilcoxon Rank Sum test, and the Least Absolute Shrinkage and Selection Operator (Lasso) method. For selecting the best classification methods in Stage 2 of an adaptive design, we examine classification methods including the recently developed machine learning approaches such as Random Forest, Lasso and Elastic-Net Regularized Generalized Linear Models (Glmnet), Support Vector Machine (SVM), Gradient Boosting Machine (GBM), and Extreme Gradient Boost- ing (XGBoost). Statistical simulations are carried out in our study to assess the performance of biomarker identification methods and the classification methods. The best identification method and the classification technique will be selected based on the True Positive Rate (TPR,also called Sensitivity) and the True Negative Rate (TNR,also called Specificity). The optimal test method for gene identification and classification method for patient grouping will be applied to the Adap- tive Signature Design (ASD) for the purpose of evaluating the performance of ASD in different situations, including simulated data and a real data set for breast cancer patients. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2018. / February 20, 2018. / Includes bibliographical references. / XuFeng Niu, Professor Directing Dissertation; Richard S. Nowakowski, University Representative; Dan McGee, Committee Member; Elizabeth Slate, Committee Member; Jinfeng Zhang, Committee Member.

With the increase in computation and data storage, there has been a vast collection of information gained with scientific measurement devices. However, with this increase in data and variety of domain applications, statistical methodology must be tailored to specific problems. This dissertation is focused on analyzing chemical information with an underlying structure. Robust fused lasso leverages information about the neighboring regression coefficient structure to create blocks of coefficients. Robust modifications are made to the mean to account for gross outliers in the data. This method is applied to near infrared spectral measurements in prediction of an aqueous analyte concentration and is shown to improve prediction accuracy. Expansion on the robust estimation and structure analysis is performed by examining graph structures within a clustered tensor. The tensor is subjected to wavelet smoothing and robust sparse precision matrix estimation for a detailed look into the covariance structure. This methodology is applied to catalytic kinetics data where the graph structure estimates the elementary steps within the reaction mechanism. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Fall Semester 2018. / October 18, 2018. / Includes bibliographical references. / Yiyuan She, Professor Directing Dissertation; Albert Stiegman, University Representative; Qing Mai, Committee Member; Eric Chicken, Committee Member.

Source: Dissertation Abstracts International, Volume: 30-02, Section: B, page: 0891. / Thesis (Ph.D.)--The Florida State University, 1968.

Source: Dissertation Abstracts International, Volume: 30-05, Section: B, page: 2460. / Thesis (Ph.D.)--The Florida State University, 1968.

Source: Dissertation Abstracts International, Volume: 31-10, Section: B, page: 6332. / Thesis (Ph.D.)--The Florida State University, 1970.

This research contributes to the theory and methods of testing hypotheses for classes of life distributions. Two classes of life distributions considered in this dissertation are: (1) The New Better Than Used (NBU) Class: The life distribution F is NBU if F(x+y)(' )(LESSTHEQ)(' )F(x)F(y) for all x, y (GREATERTHEQ) 0, where F(' )(TBOND)(' )1 - F. (2) The New Better Than Used at t(,0) (NBU-t(,0)) Class: The life distribution F is NBU-t(,0) if F(x+t(,0))(' )(LESSTHEQ)(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0. / The NBU and NBU-t(,0) classes have dual classes (New Worse Than Used and New Worse Than Used At t(,0), respectively) defined by reversing the inequality. / The NBU-t(,0) class is a new class of life distributions and contains the NBU class. We study the basic properties of the NBU-t(,0) class and propose a test of H(,0): F(x+t(,0))(' )=(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0, versus H(,A): F(x+t(,0))(' )(LESSTHEQ)(' )F(x)F(t(,0)) for all x (GREATERTHEQ) 0 and the inequality holds for some x (GREATERTHEQ) 0, based on a complete random sample X(,1), ..., X(,n) from F. Our test can also be used to test H(,0) against the NWU-t(,0) alternatives. Asymptotic relative efficiencies of our test with respect to the Hollander and Proschan (1972, Ann. Math. Statist. 43, 1136-1146) NBU test are calculated for several distributions. / We extend our test of H(,0) versus H(,A) to accommodate randomly censored data. For the censored data situation our test is based on the statistic / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where F is the Kaplan-Meier (1958, J. Amer. Statist. Assoc. 53, 457-481) estimator of(' )F. Under mild regularity conditions on the amount of censoring, a consistent test of H(,0) versus H(,A) for the randomly censored model is obtained. / In Chapter III we develop a two-sample NBU test of the null hypothesis that two distributions F and G are equal, versus the alternative that F is "more NBU" than is G. Our test is based on the statistic / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / where m and n are the sample sizes from F and G, and F(,m) and G(,n) are the empirical distributions of F and G. Asymptotic normality of T(,m,n), suitably normalized, is a direct consequence of Hoeffding's (1948, Ann. Math. Statist. 19, 293-325) U-statistic theorem. Then, using a consistent estimator of the null asymptotic variance of N(' 1/2)T(,m,n), where N = m + n, we obtain an asymptotically distribution-free test. We extend the two-sample NBU test to the k-sample case. / Our test of H(,0) versus H(,A) utilizes the Kaplan-Meier estimator. However, there are other possible estimators of the survival function for the randomly censored model. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI / Source: Dissertation Abstracts International, Volume: 43-10, Section: B, page: 3290. / Thesis (Ph.D.)--The Florida State University, 1982.

This dissertation provides a new method of treating the conservative low dose extrapolation problem. One wishes to determine the largest dose d, called the "safe" dose, for which P(F(d) (LESSTHEQ) r) (GREATERTHEQ) 1 - (eta) where F(d) is the proportion of failures, say cancers induced, at dose d by time T. F is a life distribution function, presumed to come from some class of functions F, T is prespecified, r () {0,1}, denotes the proportion of failures at doses (x,y) by fixed time T. Four extensions of the univariate class of IFR functions are introduced, differing in the way that convexity of the hazard function, H(x,y) = -ln(1-F(x,y)) is posited. The notion of dependent action is considered and a hypothesis test for its existence given. / Conservative low dose extrapolation techniques for the two most prominent classes are given. An upper bound for the hazard function is established for low doses with proofs that the bounds are sharp. / Source: Dissertation Abstracts International, Volume: 45-09, Section: B, page: 2980. / Thesis (Ph.D.)--The Florida State University, 1984.

Given that an item is of age t, the expected value of the random remaining life is called the mean residual life (MRL) at age t. We propose two new nonparametric classes of life distributions for modeling aging based on MRL. The first class of life distributions consists of those with "increasing initially, then decreasing mean residual life" (IDMRL). The IDMRL class models aging that is initially beneficial, then adverse. The second class, "decreasing, then increasing mean residual life" (DIMRL), models aging that is initially adverse, then beneficial. We present situations where IDMRL (DIMRL) distributions are useful models. We propose two testing procedures for H(,0): constant MRL (i.e., exponentiality) versus H(,1): IDMRL, but not constant MRL (or H(,1)(''): DIMRL, but not constant MRL). The first testing procedure assumes the turning point, (tau), from IMRL to DMRL is specified by the user or is known. Our IDMRL((tau)) test statistic, T(,n), is a differentiable statistical function of order 1; thus, T(,n), suitably standardized is asymptotically normal. The second procedure assumes knowledge of the proportion, (rho), of the population that "dies" at or before the turning point (knowledge of (tau) itself is not assumed). We use L-statistic theory to show our IDMRL((rho)) test statistic, V(,n)('*), appropriately standardized is asymptotically normal. The exact null distribution of V(,n)('*) is established. For each of these procedures an application is given. After this we modify the complete data tests to yield analogous censored data procedures. The standard Kaplan-Meier Estimator is a key tool that we exploit for our censored data tests. A limited Monte Carlo study investigates the censored data procedures. / Source: Dissertation Abstracts International, Volume: 45-09, Section: B, page: 2979. / Thesis (Ph.D.)--The Florida State University, 1984.

Source: Dissertation Abstracts International, Volume: 40-10, Section: B, page: 4889. / Thesis (Ph.D.)--The Florida State University, 1979.