Model averaging and dimension selection for the singular value decomposition

• 成果类型: Article
• 署名作者: Hoff, Peter D.
• 署名单位: University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle; University of Washington; University of Washington Seattle
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214506000001310
• 发表日期: 2007
• 页码: 674-685
• 关键词: Matrices

摘要

Many multivariate data-analysis techniques for an m x n matrix Y are related to the model Y = M + E, where Y is an m x 17 matrix of full rank and M is an unobserved mean matrix of rank K < (m boolean AND n). Typically the rank of M is estimated in a heuristic way and then the least-squares estimate of M is obtained via the singular value decomposition of Y, yielding an estimate that can have a very high variance. In this article we suggest a model-based alternative to the preceding approach by providing prior distributions and posterior estimation for the rank of M and the components of its singular value decomposition. In addition to providing more accurate inference, such an approach has the advantage of being extendable to more general data-analysis situations, such as inference in the presence of missing data and estimation in a generalized linear modeling framework.