# Cross additivity - an application

Sandra Saraiva Ferreira; Dário Ferreira; João Tiago Mexia

Discussiones Mathematicae Probability and Statistics (2006)

- Volume: 26, Issue: 2, page 207-219
- ISSN: 1509-9423

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topSandra Saraiva Ferreira, Dário Ferreira, and João Tiago Mexia. "Cross additivity - an application." Discussiones Mathematicae Probability and Statistics 26.2 (2006): 207-219. <http://eudml.org/doc/277050>.

@article{SandraSaraivaFerreira2006,

abstract = {We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility arises from the introduction of the concept of regions of controled posterior risk.},

author = {Sandra Saraiva Ferreira, Dário Ferreira, João Tiago Mexia},

journal = {Discussiones Mathematicae Probability and Statistics},

keywords = {cross nested designs; cross additivity; variance components; UMVUE},

language = {eng},

number = {2},

pages = {207-219},

title = {Cross additivity - an application},

url = {http://eudml.org/doc/277050},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Sandra Saraiva Ferreira

AU - Dário Ferreira

AU - João Tiago Mexia

TI - Cross additivity - an application

JO - Discussiones Mathematicae Probability and Statistics

PY - 2006

VL - 26

IS - 2

SP - 207

EP - 219

AB - We try to show that Discriminant Analysis can be considered as a branch of Statistical Decision Theory when viewed from a Bayesian approach. First we present the necessary measure theory results, next we briefly outline the foundations of Bayesian Inference before developing Discriminant Analysis as an application of Bayesian Estimation. Our approach renders Discriminant Analysis more flexible since it gives the possibility of classing an element as belonging to a group of populations. This possibility arises from the introduction of the concept of regions of controled posterior risk.

LA - eng

KW - cross nested designs; cross additivity; variance components; UMVUE

UR - http://eudml.org/doc/277050

ER -

## References

top- [1] M. Fonseca, J.T. Mexia and R. Zmyślony, Estimating and testing of variance components: an application to a grapevine experiment, Biometrical Letters 40 (1) (2003), 1-7.
- [2] J.T. Mexia, Introduction to Linear Statistical Inference, Center of Studies of Applied Mathematics, Lusófonas Editions - Lisboa 1995.
- [3] S.F. Saraiva, Inference for Orthogonal Models with Segregation, PhD Thesis, UBI - Covilhã 2006.