Publications [#380175] of Peter D. Hoff
Papers Published
- Hoff, PD. "Model averaging and dimension selection for the singular value decomposition." Journal of the American Statistical Association 102.478 (June, 2007): 674-685. [doi]
(last updated on 2026/01/13)Abstract:
Many multivariate data-analysis techniques for an m × n matrix Y are related to the model Y = M + E, where Y is an m × n matrix of full rank and M is an unobserved mean matrix of rank K < (m ∧ 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. © 2007 American Statistical Association.