Envelope model is a nascent dimension reduction technique. We focus on extending the envelope methodology to broader applications. In the first part of this thesis we propose a common reducing subspace model that can simultaneously estimating covariance, precision matrices and their differences across multiple populations. This model leads to substantial dimension reduction and efficient parameter estimation. We explicitly quantify the efficiency gain through an asymptotic analysis. In the second part, we propose a set of new mixture models called CLEMM (Clustering with Envelope Mixture Models) that is based on the widely used Gaussian mixture model assumptions. The proposed CLEMM framework and the associated envelope-EM algorithms provides the foundations for envelope methodology in unsupervised and semi-supervised learning problems. We also illustrate the performance of these models with simulation studies and empirical applications. Also, we have extended the envelope discriminant analysis from vector data to tensor data in the third part of this thesis. Another study on copula-based models for forecasting realized volatility matrix is included, which is an important financial application of estimating covariance matrices. We consider multivariate-t, Clayton, and bivariate t, Gumbel, Clayton copulas to model and forecast one-day ahead realized volatility matrices. Empirical results show that copula based models can achieve significant performance both in terms of statistical precision and economical efficiency. / A Dissertation submitted to the Department of Statistics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. / Spring Semester 2019. / April 18, 2019. / Clustering Analysis, Dimension Reduction, EM algorithm, Envelope models, Reducing subspace, Tensor classification / Includes bibliographical references. / Xin Zhang, Professor Co-Directing Dissertation; Minjing Tao, Professor Co-Directing Dissertation; Wen Li, University Representative; Fred Huffer, Committee Member.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_709850 |
| Contributors | Wang, Wenjing (author), Zhang, Xin (Professor Co-Directing Dissertation), Tao, Minjing (Professor Co-Directing Dissertation), Li, Wen (University Representative), Huffer, Fred W. (Fred William) (Committee Member), Florida State University (degree granting institution), College of Arts and Sciences (degree granting college), Department of Statistics (degree granting departmentdgg) |
| Publisher | Florida State University |
| Source Sets | Florida State University |
| Language | English, English |
| Detected Language | English |
| Type | Text, text, doctoral thesis |
| Format | 1 online resource (127 pages), computer, application/pdf |
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