### Abstract

Original language | English |
---|---|

Pages (from-to) | 140-159 |

Journal | The Annals of Statistics |

Volume | 30 |

Issue number | 1 |

Publication status | Published - 2002 |

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*The Annals of Statistics*,

*30*(1), 140-159.

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*The Annals of Statistics*, vol. 30, no. 1, pp. 140-159.

**Marginal Models for Categorial Data.** / Bergsma, W.P.; Rudas, T.

Research output: Contribution to journal › Article › Scientific › peer-review

TY - JOUR

T1 - Marginal Models for Categorial Data

AU - Bergsma, W.P.

AU - Rudas, T.

PY - 2002

Y1 - 2002

N2 - Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal log-linear parameters and describes conditions for a marginal log-linear parameter to be a smooth parameterization of the distribution and to be variation independent. Statistical models defined by imposing affine restrictions on the marginal log-linear parameters are investigated. These models generalize ordinary log-linear and multivariate logistic models. Sufficient conditions for a log-affine marginal model to be nonempty and to be a curved exponential family are given. Standard large-sample theory is shown to apply to maximum likelihood estimation of log-affine marginal models for a variety of sampling procedures.

AB - Statistical models defined by imposing restrictions on marginal distributions of contingency tables have received considerable attention recently. This paper introduces a general definition of marginal log-linear parameters and describes conditions for a marginal log-linear parameter to be a smooth parameterization of the distribution and to be variation independent. Statistical models defined by imposing affine restrictions on the marginal log-linear parameters are investigated. These models generalize ordinary log-linear and multivariate logistic models. Sufficient conditions for a log-affine marginal model to be nonempty and to be a curved exponential family are given. Standard large-sample theory is shown to apply to maximum likelihood estimation of log-affine marginal models for a variety of sampling procedures.

M3 - Article

VL - 30

SP - 140

EP - 159

JO - The Annals of Statistics

JF - The Annals of Statistics

SN - 0090-5364

IS - 1

ER -