| LDR | | 00000nam u2200205 4500 |
| 001 | | 000000434050 |
| 005 | | 20200226135802 |
| 008 | | 200131s2019 ||||||||||||||||| ||eng d |
| 020 | |
▼a 9781687905277 |
| 035 | |
▼a (MiAaPQ)AAI22619439 |
| 040 | |
▼a MiAaPQ
▼c MiAaPQ
▼d 247004 |
| 082 | 0 |
▼a 510 |
| 100 | 1 |
▼a Yang, Zikun. |
| 245 | 10 |
▼a Gaussian Regression Model Selection in High Dimension. |
| 260 | |
▼a [S.l.]:
▼b Indiana University.,
▼c 2019. |
| 260 | 1 |
▼a Ann Arbor:
▼b ProQuest Dissertations & Theses,
▼c 2019. |
| 300 | |
▼a 139 p. |
| 500 | |
▼a Source: Dissertations Abstracts International, Volume: 81-04, Section: B. |
| 500 | |
▼a Advisor: Womack, Andrew. |
| 502 | 1 |
▼a Thesis (Ph.D.)--Indiana University, 2019. |
| 506 | |
▼a This item must not be sold to any third party vendors. |
| 520 | |
▼a Statistics is a discipline focused on experimental design, data collection, inference, and presentation. Numerous statistical methodologies have become standard tools for offering insight into investigations from applied disciplines. Arguably the most fundamental and widely applied method is Gaussian linear regression model, which is a probabilistic method for modeling the relationship between a randomly distributed response and one or more explanatory covariates. One of the main challenges of building a regression model is to select a suitable model based on different criteria, and researchers oftentimes tend to choose an economic model with as few covariates possible while still maintaining good estimation or prediction properties. As the ability of collecting massive amounts of data has dramatically increased in recent years (e.g., in genomic studies, online data collection, and smart devices) a new difficulty has arisen in performing model selection in the high-dimensional regime. Here, the number of explanatory covariates is large (or even increasing) with respect to the sample size. In this thesis, I address the model section from two directions, discrete variable selection and continuous variable shrinkage. The discrete variable selection is to seek the model with the highest posterior probability conditioning on the observed data. To overcome the dilemma imposed by the growing dimensions of the model space, a truncated Poisson prior and the mixture of g[Special character(s) omitted]prior have been deployed to attain model selection consistency. For continuous variable shrinkage, the model includes all of the covariates and achieves model selection behavior by shrinking the coefficients of covariates with no or negligible effect on the outcome variable. An innovative log-Cauchy prior distribution on the local shrinkage parameter has been discovered, which yields superior theoretical advantages over competing methods while not creating a more costly computational framework. These methods should contribute to the solution of new challenges received from applied disciplines. |
| 590 | |
▼a School code: 0093. |
| 650 | 4 |
▼a Statistics. |
| 650 | 4 |
▼a Mathematics. |
| 690 | |
▼a 0463 |
| 690 | |
▼a 0405 |
| 710 | 20 |
▼a Indiana University.
▼b Statistics. |
| 773 | 0 |
▼t Dissertations Abstracts International
▼g 81-04B. |
| 773 | |
▼t Dissertation Abstract International |
| 790 | |
▼a 0093 |
| 791 | |
▼a Ph.D. |
| 792 | |
▼a 2019 |
| 793 | |
▼a English |
| 856 | 40 |
▼u http://www.riss.kr/pdu/ddodLink.do?id=T15493625
▼n KERIS
▼z 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
| 980 | |
▼a 202002
▼f 2020 |
| 990 | |
▼a ***1008102 |
| 991 | |
▼a E-BOOK |