### 抜粋

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.

元の言語 | 英語 |
---|---|

ページ（範囲） | 863-875 |

ページ数 | 13 |

ジャーナル | Statistics and Computing |

巻 | 25 |

発行部数 | 5 |

DOI | |

出版物ステータス | 出版済み - 5 28 2015 |

外部発表 | Yes |

### フィンガープリント

### All Science Journal Classification (ASJC) codes

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

### これを引用

*Statistics and Computing*,

*25*(5), 863-875. https://doi.org/10.1007/s11222-014-9458-0