The thesis aims at showing some important methods, theories and
applications about non-parametric density estimation via
regularization in univariate setting.
It gives a brief introduction to non-parametric density estimation,
and discuss several well-known methods, for example, histogram and
kernel methods. Regularized methods with penalization and shape
constraints are the focus of the thesis. Maximum entropy density
estimation is introduced and the relationship between taut string
and maximum entropy density estimation is explored. Furthermore, the
dual and primal theories are discussed and some theoretical proofs
corresponding to quasi-concave density estimation are presented.
Different the numerical methods of non-parametric density estimation
with regularization are classified and compared. Finally, a real
data experiment will also be discussed in the last part of the
thesis. / Statistics
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/709 |
| Date | 11 1900 |
| Creators | Lin, Mu |
| Contributors | Mizera, Ivan (Department of Mathematical and Statistical Sciences), Karunamuni, Rohana (Department of Mathematical and Statistical Sciences), Li, Pengfei (Department of Mathematical and Statistical Sciences), Leuangthong, Oy (Department of Civil and Environmental Engineering) |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 402380 bytes, application/pdf |
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