Editing Loss function (section)

==Constructing loss and objective functions==
{{See also|Scoring rule}}
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation.  In other situations, the decision maker’s preference must be elicited and represented by a scalar-valued function (called also  [[utility]] function) in a form  suitable for optimization — the problem that [[Ragnar Frisch]] has highlighted in his [[Nobel Prize]] lecture.<ref>{{cite book| first=Ragnar|last=Frisch|date=1969 |title= The Nobel Prize–Prize Lecture|chapter=From utopian theory to practical applications: the case of econometrics|url=https://www.nobelprize.org/prizes/economic-sciences/1969/frisch/lecture/|access-date=15 February 2021}}</ref>
The existing methods for constructing objective functions are collected in the proceedings of two dedicated conferences.<ref name="TangianGruber1997">{{Cite book
|last1=Tangian |first1=Andranik |last2=Gruber |first2=Josef |date=1997
|title= Constructing Scalar-Valued Objective Functions. Proceedings of the Third International Conference on Econometric Decision Models: Constructing Scalar-Valued Objective Functions, University of Hagen, held in Katholische Akademie Schwerte September 5–8, 1995|series= Lecture Notes in Economics and Mathematical Systems |volume=453|isbn= 978-3-540-63061-6 |doi= 10.1007/978-3-642-48773-6
|publisher=Springer |location=Berlin }}</ref><ref name="TangianGruber2002">{{Cite book
|last1=Tangian |first1=Andranik  |last2=Gruber |first2=Josef |date=2002
|title= Constructing and Applying Objective Functions. Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, held in Haus Nordhelle, August, 28 — 31, 2000
|series= Lecture Notes in Economics and Mathematical Systems |volume=510
|publisher=Springer |location=Berlin|isbn= 978-3-540-42669-1 |doi= 10.1007/978-3-642-56038-5 }}</ref>
In particular, [[Andranik Tangian]] showed that the most usable objective functions — quadratic and additive — are determined by a few [[Principle of indifference|indifference]] points. He used this property in the models for constructing these objective functions from either [[ordinal utility|ordinal]] or [[cardinal utility|cardinal]] data that were elicited through computer-assisted interviews with decision makers.<ref name="Tangian2002">{{Cite journal|last=Tangian |first=Andranik |year=2002|title= Constructing a quasi-concave quadratic objective function from interviewing a decision maker|journal= European Journal of Operational Research |volume=141 |issue=3 |pages=608–640 |doi=10.1016/S0377-2217(01)00185-0 |s2cid= 39623350 }}</ref><ref name="Tangian2004additiveUtility">{{Cite journal|last=Tangian |first=Andranik |year=2004|title= A model for ordinally constructing additive objective functions|journal= European Journal of Operational Research |volume=159 |issue=2 |pages=476–512|doi = 10.1016/S0377-2217(03)00413-2  | s2cid= 31019036 }}</ref> 
Among other things, he constructed  objective functions to optimally distribute budgets for 16 Westfalian universities<ref name="Tangian2004universityBudgets">{{Cite journal |last=Tangian |first=Andranik |year=2004 |title= Redistribution of university budgets with respect to the status quo |journal= European Journal of Operational Research |volume=157 |issue=2 |pages=409–428|doi = 10.1016/S0377-2217(03)00271-6 }}</ref>
and the European subsidies for equalizing unemployment rates among 271 German regions.<ref name="Tangian2008RegionalEnemployment">{{Cite journal|last=Tangian |first=Andranik |year=2008
|title= Multi-criteria optimization of regional employment policy: A simulation analysis for Germany |journal= Review of Urban and Regional Development |volume=20 |issue=2|pages=103–122 |url= https://onlinelibrary.wiley.com/doi/10.1111/j.1467-940X.2008.00144.x |doi = 10.1111/j.1467-940X.2008.00144.x }}</ref>