Factor Models with Real Data: a Robust Estimation of the Number of Factors
Autor: | Mattia Zorzi, Valentina Ciccone, Augusto Ferrante |
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Jazyk: | angličtina |
Rok vydání: | 2017 |
Předmět: |
0209 industrial biotechnology
Rank (linear algebra) Covariance matrix Matrix norm duality theory factor analysis 02 engineering and technology Positive-definite matrix Convex optimization Computer Science Applications Matrix decomposition Matrix (mathematics) 020901 industrial engineering & automation Control and Systems Engineering Optimization and Control (math.OC) nuclear norm FOS: Mathematics Applied mathematics Symmetric matrix Electrical and Electronic Engineering Mathematics - Optimization and Control Mathematics Factor analysis |
Popis: | Factor models are a very efficient way to describe high dimensional vectors of data in terms of a small number of common relevant factors. This problem, which is of fundamental importance in many disciplines, is usually reformulated in mathematical terms as follows. We are given the covariance matrix Sigma of the available data. Sigma must be additively decomposed as the sum of two positive semidefinite matrices D and L: D | that accounts for the idiosyncratic noise affecting the knowledge of each component of the available vector of data | must be diagonal and L must have the smallest possible rank in order to describe the available data in terms of the smallest possible number of independent factors. In practice, however, the matrix Sigma is never known and therefore it must be estimated from the data so that only an approximation of Sigma is actually available. This paper discusses the issues that arise from this uncertainty and provides a strategy to deal with the problem of robustly estimating the number of factors. arXiv admin note: text overlap with arXiv:1708.00401 |
Databáze: | OpenAIRE |
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