Loss function: Difference between revisions

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|publisher=Wiley Classics Library |year=2004 |orig-year=1970

|isbn=978-0-471-68029-1 |mr=2288194

}}</ref><ref>{{citeq|Q55953130}}</ref> of the decision rule ''δ'' and the parameter ''θ''. Here the decision rule depends on the outcome of ''X''. The risk function is given by:

}}</ref><ref>{{cite book

|last=Robert |first=Christian P.

|title=The Bayesian Choice

|publisher=Springer |___location=New York

|year=2007|edition=2nd

|doi=10.1007/0-387-71599-1 |isbn=978-0-387-95231-4 |mr=1835885

|series=Springer Texts in Statistics

}}</ref> of the decision rule ''δ'' and the parameter ''θ''. Here the decision rule depends on the outcome of ''X''. The risk function is given by:

: <math>R(\theta, \delta) = \operatorname{E}_\theta L\big( \theta, \delta(X) \big) = \int_X L\big( \theta, \delta(x) \big) \, \mathrm{d} P_\theta (x) .</math>