Model averaging and dimension selection for the singular value decomposition

Details Model averaging and dimension selection for the singular value decomposition Model averaging and dimension selection for the singular value decomposition

2006-09-01

arxiv.org/abs/math/0609042v1

Mathematics

Statistics Theory

Scientific paper

Many multivariate data analysis techniques for an $m\times n$ matrix $\m Y$ are related to the model $\m Y = \m M +\m E$, where $\m Y$ is an $m\times n$ matrix of full rank and $\m M$ is an unobserved mean matrix of rank $K< (m\wedge n)$. Typically the rank of $\m M$ is estimated in a heuristic way and then the least-squares estimate of $\m M$ is obtained via the singular value decomposition of $\m Y$, yielding an estimate that can have a very high variance. In this paper we suggest a model-based alternative to the above approach by providing prior distributions and posterior estimation for the rank of $\m M$ 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.

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