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

Abstract

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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.

How to cite

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Sandra 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

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  1. [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. [2] J.T. Mexia, Introduction to Linear Statistical Inference, Center of Studies of Applied Mathematics, Lusófonas Editions - Lisboa 1995. 
  3. [3] S.F. Saraiva, Inference for Orthogonal Models with Segregation, PhD Thesis, UBI - Covilhã 2006. 

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