Sparse estimation via nonconcave penalized likelihood in factor analysis model

Kei Hirose, Michio Yamamoto

Research output: Contribution to journalArticlepeer-review

45 Citations (Scopus)


We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates cannot be obtained when the number of variables is much larger than the number of observations. Furthermore, even if the maximum likelihood estimates are available, the rotation technique does not often produce a sufficiently sparse solution. In order to handle these problems, this paper introduces a penalized likelihood procedure that imposes a nonconvex penalty on the factor loadings. We show that the penalized likelihood procedure can be viewed as a generalization of the traditional two-step approach, and the proposed methodology can produce sparser solutions than the rotation technique. A new algorithm via the EM algorithm along with coordinate descent is introduced to compute the entire solution path, which permits the application to a wide variety of convex and nonconvex penalties. Monte Carlo simulations are conducted to investigate the performance of our modeling strategy. A real data example is also given to illustrate our procedure.

Original languageEnglish
Pages (from-to)863-875
Number of pages13
JournalStatistics and Computing
Issue number5
Publication statusPublished - May 28 2015
Externally publishedYes


  • Coordinate descent algorithm
  • Factor analysis
  • Nonconvex penalty
  • Penalized likelihood
  • Rotation technique

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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