archives@tulane.edu / In this thesis, we examine models of scale invariant behavior in univariate, multivariate, and high-dimensional settings from the viewpoint of wavelet-based statistical inference, and construct a new class of models called operator fractional Lévy motion.
The first part of this work pertains to tempered fractional Brownian motion (tfBm), a model that displays transient scale invariant behavior. We use wavelets to construct the first estimation procedure for tfBm as well as a simple and computationally efficient hypothesis test and study their properties.
In the second part of this thesis, we construct a new class of non-Gaussian second-order scale invariance models called operator fractional Lévy motion (ofLm) and study its probabilistic behavior. We then study asymptotic properties of wavelet eigenanalysis estimation applied to ofLm and examine its performance.
In the last portion of this work, we study the mathematical framework of wavelet eigenanalysis in a multivariate setting with a view towards high-dimensional scale invariance modeling. We then proceed to conduct wavelet-based eigenanalysis in a high-dimensional setting, and conclude with some computational experiments. / 1 / Benjamin Boniece
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_106640 |
| Date | January 2019 |
| Contributors | Boniece, Benjamin (author), (author), Didier, Gustavo (Thesis advisor), (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution), NULL (Degree granting institution) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | electronic, pages: 199 |
| Rights | No embargo, Copyright is in accordance with U.S. Copyright law. |
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