The problem of minimax mutual prediction is considered for multinomial random variables with the loss function being a linear combination of quadratic losses connected with prediction of particular variables. The basic parameter of the minimax mutual predictor is determined by numerical solution of some equation.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-1, author = {Stanis\l aw Trybu\l a}, title = {Minimax mutual prediction of multinomial random variables}, journal = {Applicationes Mathematicae}, volume = {30}, year = {2003}, pages = {371-377}, zbl = {1051.62012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-1} }
Stanisław Trybuła. Minimax mutual prediction of multinomial random variables. Applicationes Mathematicae, Tome 30 (2003) pp. 371-377. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am30-4-1/