Browsing by Author "Min Kang, Committee Member"
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- An Algorithm for Computing the Perron Root of a Nonnegative Irreducible Matrix(2007-03-09) Chanchana, Prakash; Carl D. Meyer, Committee Chair; Ernie L. Stitzinger, Committee Member; Zhilin Li, Committee Member; Min Kang, Committee MemberWe present a new algorithm for computing the Perron root of a nonnegative irreducible matrix. The algorithm is formulated by combining a reciprocal of the well known Collatz's formula with a special inverse iteration algorithm discussed in [10, Linear Algebra Appl., 15 (1976), pp 235-242]. Numerical experiments demonstrate that our algorithm is able to compute the Perron root accurately and faster than other well known algorithms; in particular, when the size of the matrix is large. The proof of convergence of our algorithm is also presented.
- Essays on Multivariate Stochastic Volatility Models Using Wishart Processes: A General Discussion and Dimension Reduction by Latent Factor Structures.(2010-08-16) Ku, Yu-Cheng; Peter Bloomfield, Committee Chair; Sujit Ghosh, Committee Member; Brian Reich, Committee Member; Min Kang, Committee Member; Ronald Gallant, Committee Member
- Financial Risk Management: Portfolio Optimization.(2011-02-18) Yang, Song; Tao Pang, Committee Chair; Negash Medhin, Committee Member; Peter Bloomfield, Committee Member; Min Kang, Committee Member
- Investigation of Different Input Noise Types in Linear and Nonlinear Stochastic Neural Models.(2010-07-15) Arai, Mamiko; Charles Smith, Committee Chair; Mark White, Committee Member; Jason Osborne, Committee Member; Min Kang, Committee Member
- Mobile Ad-hoc Networks: Mobility-induced Metrics, Performance Analysis, and System Design(2009-12-04) Cai, Han; Do Young Eun, Committee Chair; Michael Devetsikiotis, Committee Member; Mihail Sichitiu, Committee Member; Min Kang, Committee MemberMobile Ad-hoc Network (MANET), a type of self-configuring wireless ad-hoc network, comprises of mobile elements equipped with wireless communication devices. The mobility pattern of mobile nodes and the packet forwarding strategy crucially decide MANET performance. The node mobility leads to time-varying network topology. Conventional routing schemes fails due to the infeasibility to set up the end-toend path before data transmission. The mobility pattern affects system performance through mobility-induced metrics such as contact time and inter-meeting time. These metrics are critical in determining the MANET performance, as well as choosing various scheduling/forwarding algorithms. In this dissertation, we study the effect of mobility patterns on the MANET performance through the mobility-induced metrics, e.g., inter-meeting time. The intermeeting time is typically assumed to be exponentially distributed in MANET performance studies. However, recent empirical results disclose clear power-law behavior of inter-meeting time distribution. This outright discrepancy potentially undermines our understanding of the performance tradeoffs in MANET obtained under the assumed inter-meeting time with exponential distribution, and thus calls for further study on the power-law (or more generally, non-exponential) inter-meeting time including its fundamental cause, mobility modeling, and its effect. We first prove that the finite/infinite domain with respect to the time scale of interest critically decides the exponential/power-law tail of the inter-meeting time distribution. We then show a convex ordering relationship among inter-meeting times of various mobility models indexed by their degrees of correlation, which is in good agreement with the ordering of network performance under a set of mobility patterns whose inter-meeting time distributions have power-law ‘head’ followed by exponential ‘tail’. Finally, we analyze various characteristics of the relative mobility of a random pair of nodes in MANET to show that they produce inter-meeting time with different aging properties. The aging property allows us to establish for the first time that the approach based on exponential inter-meeting time assumption can always underestimate or over-estimate the actual system performance, under stochastic mobility patterns with specific aging properties. Our results also provide theoretic guidelines on how to exploit the memory structure toward better design of protocols under general mobility.
- Path Dependent Stochastic Models and Their Applications in Finance and Communications(2008-07-25) Yang, Yipeng; Zhilin Li, Committee Member; Min Kang, Committee Member; Robert T. Buche, Committee Co-Chair; Tao Pang, Committee Chair
- Robust Minimum Density Estimators and Stochastic Resonance for Classification Algorithms(2009-08-13) Heller, Martin; Kazufumi Ito, Committee Chair; Min Kang, Committee Member; Charlie Smith, Committee Member; Ralph Smith, Committee MemberThe class of Robust Minimum Density Estimators (RMDE’s) are a subset of the Minimum Density Estimators (MDE). Unlike most statistical techniques, RMDE’s treat a sample as a single observation of a random distribution function. The deviance of a small number of observations does not change the general shape of the random distribution function. As the RMDE finds estimators based on the general shape of the random distribution function, the RMDE has a great resistance to outliers. Asymptotic results of the RMDE are presented including consistency and bounds on the variance function. Once the asymptotic results are presented, the generality of the estimator is presented. Techniques of parameter estimation and regression specific to the RMDE are developed. Simulations are presented to compare the RMDE estimator with standard estimation methods with and without the addition of outliers. The methods are then extended to regression problems which does not differ for linear, nonlinear regression problems or even heteroscedastic errors. Leveraging the capabilities of the RMDE is the adaptation of Bayesian analysis to create an alternative posterior distribution. By exploiting a density associated with the RMDE estimator, a posterior distribution can be created which is incredibly robust to outliers in datasets. Simulations are used to compare the regular Bayesian posterior distribution with the RMDE posterior distribution. Techniques to implement standard Bayesian methods using the RMDE posterior distribution are described. A discussion of simulating from the posterior distribution, sequential updating of the posterior, and creation of Bayesian credible regions is presented.
