A characterization of saturated designs for factorial experiments

Roberto Fontana; Fabio Rapallo; Maria Piera Rogantin

doi:10.1016/j.jspi.2013.10.011

A characterization of saturated designs for factorial experiments

Roberto Fontana
, Fabio Rapallo
, Maria Piera Rogantin

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

Abstract

In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. Exploiting the identification of a fraction with a binary contingency table, we define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is based on combinatorial algebraic objects, namely the circuit basis of the toric ideal associated to the design matrix of the model.

Original language	English
Pages (from-to)	204-211
Number of pages	8
Journal	Journal of Statistical Planning and Inference
Volume	147
DOIs	https://doi.org/10.1016/j.jspi.2013.10.011
Publication status	Published - Apr 2014
Externally published	Yes

Keywords

Circuits
Estimability
Graver basis
Linear models
Universal Markov basis

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10.1016/j.jspi.2013.10.011

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title = "A characterization of saturated designs for factorial experiments",

abstract = "In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. Exploiting the identification of a fraction with a binary contingency table, we define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is based on combinatorial algebraic objects, namely the circuit basis of the toric ideal associated to the design matrix of the model.",

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author = "Roberto Fontana and Fabio Rapallo and Rogantin, \{Maria Piera\}",

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doi = "10.1016/j.jspi.2013.10.011",

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AU - Fontana, Roberto

AU - Rapallo, Fabio

AU - Rogantin, Maria Piera

PY - 2014/4

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AB - In this paper we study saturated fractions of factorial designs under the perspective of Algebraic Statistics. Exploiting the identification of a fraction with a binary contingency table, we define a criterion to check whether a fraction is saturated or not with respect to a given model. The proposed criterion is based on combinatorial algebraic objects, namely the circuit basis of the toric ideal associated to the design matrix of the model.

KW - Circuits

KW - Estimability

KW - Graver basis

KW - Linear models

KW - Universal Markov basis

UR - https://www.scopus.com/pages/publications/84892496651

U2 - 10.1016/j.jspi.2013.10.011

DO - 10.1016/j.jspi.2013.10.011

M3 - Article

SN - 0378-3758

VL - 147

SP - 204

EP - 211

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

ER -

A characterization of saturated designs for factorial experiments

Abstract

Keywords

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