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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher
On The Testing And Estimation Of High-Dimensional Covariance Matrices, Thomas Fisher
All Dissertations
Many applications of modern science involve a large number of parameters. In
many cases, the number of parameters, p, exceeds the number of observations,
N. Classical multivariate statistics are based on the assumption that the
number of parameters is fixed and the number of observations is large. Many of
the classical techniques perform poorly, or are degenerate, in high-dimensional
situations.
In this work, we discuss and develop statistical methods for inference of
data in which the number of parameters exceeds the number of observations.
Specifically we look at the problems of hypothesis testing regarding and the
estimation of the covariance …
Integer-Valued Time Series And Renewal Processes, Yunwei Cui
Integer-Valued Time Series And Renewal Processes, Yunwei Cui
All Dissertations
This research proposes a new but simple model for stationary time series of integer counts. Previous work in the area has focused on mixture and thinning methods and links to classical time series autoregressive moving-average difference equations; in contrast, our methods use a renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such processes, stationary series with binomial, Poisson, geometric, or any other discrete marginal distribution can be readily constructed. The model class proposed is parsimonious, non-Markov, and readily generates series with either short or long memory autocovariances. The model can be fitted with …
Pattern Recognition For Command And Control Data Systems, Jason Schwier
Pattern Recognition For Command And Control Data Systems, Jason Schwier
All Dissertations
To analyze real-world events, researchers collect observation data from an underlying process and construct models to represent the observed situation. In this work, we consider issues that affect the construction and usage of a specific type of model. Markov models are commonly used because their combination of discrete states and stochastic transitions is suited to applications with both deterministic and stochastic components. Hidden Markov Models (HMMs) are a class of Markov model commonly used in pattern recognition. We first demonstrate how to construct HMMs using only the observation data, and no a priori information, by extending a previously developed approach …
Time Series Analysis: A New Look At Some Old Problems, Ferebee Tunno
Time Series Analysis: A New Look At Some Old Problems, Ferebee Tunno
All Dissertations
This dissertation gives a comprehensive report of my doctoral research in time series analysis from summer 2006 to spring 2009. It is comprised of two main efforts: interval estimation for an autoregressive parameter and arc length tests for equivalent ARIMA dynamics. Such problems are traditional in statistics, but three new theorems and several simulations are presented here that help elucidate new ways to handle them.
Tandem Queues With Non-Stationary Arrivals, Senthil Balaji Girimurugan
Tandem Queues With Non-Stationary Arrivals, Senthil Balaji Girimurugan
All Theses
We consider a network of K queues in tandem labeled Q1, Q2, ..,QK. The arrivals to Q 1 form a non-homogeneous Poisson process whose intensity is periodic. We conjecture that asymptotically the arrival process Aj to Qj, j= 1,2,..,K is cycle stationary. In addition, we conjecture that asymptotically as 'j' gets larger, the arrival process at the jth queue gets closer to a stationary point process. Hence, the queue performance measures become more stationary as 'j' increases. We perform Monte-Carlo simulations and design statistical tests whose results support the conjecture.