Physical Sciences and Mathematics Commons^™

Wavelet Factorization Via A Homogenization Analogy For Solutions Of Linear Systems, Andrea Van Sickle

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A system of linear equations can be solved using a factorization method that produces a wavelet structure and is akin to a homogenization process used in determining the solution of differential equations. The method is dependant on the particular structure of Hadamard matrices and their implementation in a similarity transform. This paper details the development of such a method for systems of size 2n x 2n, including establishing the theoretical underpinnings necessary to define an orthogonal transform. Also, we present the development of an algorithm to implement the method for a simple 2 x 2 system, which will then be …

Simulation Study Of Estimation And Inference In Factor Analysis: Normal And Non-Normal Noise Distributions, Ping Zhang

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Objective: To study the estimation and inference m factor analyses when the data have normal or non-normal noise distributions.

Methods: Population data were created in package R with a specified number of factors, factor structure and observable variables with known loadings. Then, repeated simple random samples (SRS's) were taken from the population, independently. The maximum likelihood method with varimax rotation was used to perform factor analysis and inference on each sampled dataset. Factor loadings were estimated to determine if the estimation of the loadings was (approximately) unbiased and/or efficient for each specified population and chi-square x2-statistics were obtained to test …

Special Classification Models For Lichens In The Pacific Northwest, Janeen Ardito

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A common problem in ecological studies is that of determining where to look for rare species. This paper shows how statistical models, such as classification trees, may be used to assist in the design of probability-based surveys for rare species using information on more abundant species that are associated with the rare species. This model assisted approach to survey design involves first building models for the more abundant species. The models are then used to determine stratifications for the rare species that are associated with the more abundant species. The goal of this approach is to increase the number of …

Wavelet Analysis Of Magnetometer Data, Inga Maslova

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The wavelet analysis of the ground-based magnetograms' records is performed in this project. We explore the records from low, medium and high latitude stations during a calm period and a stormy one. Different methods for detecting and estimating the tail index of heavy-tailed distributions are compared. A detailed analysis of the properties of the distributions of the discrete wavelet transform coefficients of magnetometer data is presented. Conclusions on the tail index estimation techniques and the distribution of the discrete wavelet transform coefficients are made.