acase@tulane.edu / In this thesis, we tackle the statistical problem of demixing a multivariate stochastic process made up of independent, fractional process entries. We consider both Gaussian and non-Gaussian frameworks. The observable, mixed process is then a multivariate fractional stochastic process. In particular, when the components of the unmixed process are self-similar, the mixed process is operator self-similar. Multivariate mixed fractional processes are parameterized by a vector of Hurst parameters and a mixing matrix. We propose a 2-step wavelet-based estimation method to produce estimators of both the demixing matrix and the Hurst parameters. In the first step, an estimator of the demixing matrix is obtained by applying a classical joint diagonalization algorithm to two wavelet variance matrices of the mixed process. In the second step, a univariate-like wavelet regression method is applied to each entry of the demixed process to provide estimators of each individual Hurst parameter. The limiting distribution of the estimators is established for both Gaussian and nonGaussian (Rosenblatt-like) instances. Monte Carlo experiments show that the finite sample estimation performance is very satisfactory. As an application, we model bivariate series of annual tree ring measurements from bristlecone pine trees in White Mountains, California. / 1 / Hui Li
| Identifer | oai:union.ndltd.org:TULANE/oai:http://digitallibrary.tulane.edu/:tulane_77021 |
| Date | January 2017 |
| Contributors | Li, Hui (author), Didier, Gustavo (Thesis advisor), School of Science & Engineering Mathematics (Degree granting institution) |
| Publisher | Tulane University |
| Source Sets | Tulane University |
| Language | English |
| Detected Language | English |
| Type | Text |
| Format | electronic, 110 |
| Rights | No embargo, Copyright is in accordance with U.S. Copyright law. |
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