## Abstract

Generalized iterative scaling (GIS) has become a popular method for getting the maximum likelihood estimates for log-linear models. It is basically a sequence of successive I-projections onto sets of probability vectors with some given linear combinations of probability vectors. However, when a sequence of successive I-projections are applied onto some closed and convex sets (e.g., marginal stochastic order), they may not lead to the actual solution. In this manuscript, we present a unified generalized iterative scaling (UGIS) and the convergence of this algorithm to the optimal solution is shown. The relationship between the UGIS and the constrained maximum likelihood estimation for log-linear models is established. Applications to constrained Poisson regression modeling and marginal stochastic order are used to demonstrate the proposed UGIS. Crown

Original language | English |
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Pages (from-to) | 1066-1078 |

Number of pages | 13 |

Journal | Computational Statistics and Data Analysis |

Volume | 54 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Apr 2010 |

## Scopus Subject Areas

- Statistics and Probability
- Computational Mathematics
- Computational Theory and Mathematics
- Applied Mathematics