Thesis (Ph. D.)--Physics, Georgia Institute of Technology, 2005. / You, Li, Committee Member ; Buck, John A., Committee Member ; Kvam, Paul, Committee Member ; Kennedy, Brian, Committee Member ; Trebino, Rick, Committee Chair. Vita. Includses bibliographical references.

Thesis (M.S.)--Florida State University, 2004. / Advisor: Dr. James J. O'Brien, Florida State University, College of Arts and Sciences, Dept. of Meteorology. Title and description from dissertation home page (viewed Jan. 12, 2005). Includes bibliographical references.

Thesis (Ph. D.)--University of California, San Diego, 2000. / Vita. Includes bibliographical references (leaves 206-209).

Thesis (M.S. in Operations Research) Naval Postgraduate School, March 1997. / Thesis advisor, Donald P. Gaver. Includes bibliographical references (p. 35). Also available online.

No description available.

Models governing stochasticity in various systems are typically calibrated from data, therefore are subject to statistical errors/uncertainties which can lead to inferior decision making. This thesis develops statistically and computationally efficient data-driven methods for problems in stochastic simulation and optimization to quantify and hedge impacts of these uncertainties. The first half of the thesis focuses on efficient methods for tackling input uncertainty which refers to the simulation output variability arising from the statistical noise in specifying the input models. Due to the convolution of the simulation noise and the input noise, existing bootstrap approaches consist of a two-layer sampling and typically require substantial simulation effort. Chapter 2 investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort is reduced, and explicitly identify the procedural specifications in our framework that guarantee relative consistency in the estimation, and the corresponding optimal simulation budget allocations. In Chapter 3 we study an optimization-based approach to construct confidence intervals for simulation outputs under input uncertainty. This approach computes confidence bounds from simulation runs driven by probability weights defined on the data, which are obtained from solving optimization problems under suitably posited averaged divergence constraints. We illustrate how this approach offers benefits in computational efficiency and finite-sample performance compared to the bootstrap and the delta method. While resembling distributionally robust optimization, we explain the procedural design and develop tight statistical guarantees via a generalization of the empirical likelihood method. The second half develops uncertainty quantification techniques for certifying solution feasibility and optimality in data-driven optimization. Regarding optimality, Chapter 4 proposes a statistical method to estimate the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging, resampled sample average approximation (SAA). We show how this approach leads to valid statistical confidence bounds for non-smooth optimization. We also demonstrate its statistical efficiency and stability that are especially desirable in limited-data situations. We present our theory that views SAA as a kernel in an infinite-order symmetric statistic. Regarding feasibility, Chapter 5 considers data-driven optimization under uncertain constraints, where solution feasibility is often ensured through a "safe" reformulation of the constraints, such that an obtained solution is guaranteed feasible for the oracle formulation with high confidence. Such approaches generally involve an implicit estimation of the whole feasible set that can scale rapidly with the problem dimension, in turn leading to over-conservative solutions. We investigate validation-based strategies to avoid set estimation by exploiting the intrinsic low dimensionality of the set of all possible solutions output from a given reformulation. We demonstrate how our obtained solutions satisfy statistical feasibility guarantees with light dimension dependence, and how they are asymptotically optimal and thus regarded as the least conservative with respect to the considered reformulation classes.

No description available.

Ringo M.H. Ho. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 75-81). / ACKNOWLEDGMENT --- p.2 / ABSTRACT --- p.3 / TABLE OF CONTENTS --- p.5 / LIST OF TABLES --- p.8 / Chapter CHAPTER 1 --- PREVIOUS STUDIES ON USING PROCRUSTES ROTATION TO ASSESS FACTORIAL INVARIANCE --- p.10 / Factorial invariance problem --- p.10 / Procrustes rotation with congruent coefficient as a way to test factorial invariance --- p.11 / Quantifying the Procrustes fit --- p.14 / Outline of the present study --- p.15 / Chapter CHAPTER 2 --- A CRITICAL EVALUATION OF THE PERMUTATION METHOD --- p.18 / Introduction --- p.18 / Method --- p.19 / Results and Discussions --- p.21 / Chapter CHAPTER 3 --- BOOTSTRAP TESTING PROCEDURE FOR A FULLY SPECIFIED TARGET --- p.24 / Introduction --- p.24 / A brief introduction to the bootstrap procedure --- p.24 / The bootstrap testing procedure for a fully specified target --- p.26 / Method --- p.28 / Results and Discussions --- p.28 / Chapter CHAPTER 4 --- BOOTSTRAP TESTING FOR A PARTIALLY SPECIFIED TARGET --- p.33 / Introduction --- p.33 / The bootstrap testing procedure for a partially specified target --- p.36 / Method --- p.38 / Quantifying the fit - congruence coefficients for the partial target rotation --- p.39 / Results and Discussions --- p.40 / Chapter CHAPTER 5 --- FURTHER EXTENSIONS OF THE BOOTSTRAP METHOD --- p.45 / Introduction --- p.45 / First extension - when correlation matrix is used --- p.45 / The modified bootstrap procedure --- p.45 / Method --- p.48 / Results and Discussions --- p.48 / Second extension - when raw data of the target sample is not available --- p.49 / The conditional bootstrap procedure for a fully specified target --- p.49 / Method --- p.50 / Results and Discussions --- p.51 / Chapter CHAPTER 6 --- THREE REAL EXAMPLES --- p.54 / Example 1 - Testing factorial invariance of CPAI between two random split samples --- p.54 / Results --- p.55 / Example 2 - Testing factorial invariance of CPAI between Chinese males and females --- p.56 / Results --- p.57 / Example 3 - Cross-cultural comparison of the Big Five Model between U. S. and Chinese samples --- p.58 / Results --- p.59 / Chapter CHAPTER 7 --- CONCLUSIONS --- p.62 / Practical remarks on the bootstrap procedure --- p.62 / A note on the transformation on the sample for constructing correct resampling space --- p.64 / Remarks on utilizing the congruence coefficients --- p.65 / How good are the congruence coefficients in detecting discrepancy between two factor structures? --- p.68 / Rule of thumb for factor congruence coefficient in checking factor replicability --- p.68 / Sample size requirement --- p.69 / Limitations of the present study --- p.70 / Direction of future studies --- p.71 / Concluding remarks --- p.73 / REFERENCES --- p.75 / NOTES --- p.82 / APPENDIX1 --- p.83 / TABLES 1 TO TABLES17 --- p.84

Cheung, Yu Hin Ray. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 47-49). / Abstracts in English and Chinese. / Chapter CHAPTER ONE: --- INTRODUCTION --- p.1 / Chapter CHAPTER TWO: --- A UNIFIED BOOTSTRAP PROCEDURE --- p.7 / Chapter CHAPTER THREE: --- A SIMULATION STUDY --- p.10 / Chapter CHAPTER FOUR: --- RESULTS --- p.18 / Chapter CHAPTER FIVE: --- DISCUSSION --- p.33 / Chapter CHAPTER SIX: --- CONCLUSION --- p.37 / APPENDICES --- p.38 / REFERENCES --- p.46

The focus of this thesis is extremal dependence among spatial observations. In particular, this research extends the notion of the extremogram to the spatial process setting. Proposed by Davis and Mikosch (2009), the extremogram measures extremal dependence for a stationary time series. The versatility and flexibility of the concept made it well suited for many time series applications including from finance and environmental science. After defining the spatial extremogram, we investigate the asymptotic properties of the empirical estimator of the spatial extremogram. To this end, two sampling scenarios are considered: 1) observations are taken on the lattice and 2) observations are taken on a continuous region in a continuous space, in which the locations are points of a homogeneous Poisson point process. For both cases, we establish the central limit theorem for the empirical spatial extremogram under general mixing and dependence conditions. A high level overview is as follows. When observations are observed on a lattice, the asymptotic results generalize those obtained in Davis and Mikosch (2009). For non-lattice cases, we define a kernel estimator of the empirical spatial extremogram and establish the central limit theorem provided the bandwidth of the kernel gets smaller and the sampling region grows at proper speeds. We illustrate the performance of the empirical spatial extremogram using simulation examples, and then demonstrate the practical use of our results with a data set of rainfall in Florida and ground-level ozone data in the eastern United States. The second part of the thesis is devoted to bootstrapping and variance estimation with a view towards constructing asymptotically correct confidence intervals. Even though the empirical spatial extremogram is asymptotically normal, the limiting variance is intractable. We consider three approaches: for lattice data, we use the circular bootstrap adapted to spatial observations, jackknife variance estimation, and subsampling variance estimation. For data sampled according to a Poisson process, we use subsampling methods to estimate the variance of the empirical spatial extremogram. We establish the (conditional) asymptotic normality for the circular block bootstrap estimator for the spatial extremogram and show L2 consistency of the variance estimated by jackknife and subsampling. Then, we propose a portmanteau style test to check the existence of extremal dependences at multiple lags. The validity of confidence intervals produced from these approaches and a portmanteau style test are demonstrated through simulation examples. Finally, we illustrate this methodology to two data sets. The first is the amount of rainfall over a grid of locations in northern Florida. The second is ground-level ozone in the eastern United States, which are recorded on an irregularly spaced set of stations.