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Research Seminar Series in Statistics and Mathematics

Wirtschaftsuniversität Wien, Departments 4 D4.4.00811:00 - 12:10

Type Lecture / discussion
SpeakerTobias Fissler (Department of Mathematics, Imperial College London)
Organizer Institut für Statistik und Mathematik

To­bias Fissler (De­part­ment of Mathem­at­ics, Im­per­ial Col­lege Lon­don) about "The Eli­cit­a­tion Prob­lem or The Quest of Com­par­ing Fore­casts in a Mean­ing­ful Way"

The In­sti­tute for Stat­ist­ics and Mathem­at­ics (De­part­ment of Fin­ance, Ac­count­ing and Stat­ist­ics) cor­di­ally in­vites every­one in­ter­ested to at­tend the talks in our Re­search Sem­inar Ser­ies, where in­ter­na­tion­ally renowned schol­ars from lead­ing uni­versit­ies present and dis­cuss their (work­ing) pa­pers.

The list of talks for the win­ter term 2018/19 is avail­able via the fol­low­ing link: ht­tps://­math/ressem­inar

A proven strategy in de­cision-­mak­ing to cope with un­known or un­cer­tain fu­ture events is to rely on fore­casts for these events. Examples range from weather fore­casts for ag­ri­cul­ture, air­lines or a con­veni­ent every­day life, to fore­casts for sup­ply and de­mand in a busi­ness con­text, to risk-assess­ment in fin­ance or pre­dic­tions for GDP growth and in­fla­tion for pruden­tial eco­nomic policy. In the pres­ence of mul­tiple dif­fer­ent fore­casts, a core chal­lenge is to assess their re­l­at­ive qual­ity and to even­tu­ally rank them in terms of their his­toric per­form­ance. This calls for an ac­cur­acy meas­ure which is com­monly given in terms of a loss func­tion spe­cify­ing the dis­crep­ancy between a fore­cast and the ac­tual ob­ser­va­tion. Examples in­clude the zer­o-one loss, the ab­so­lute loss or the squared loss. If the ul­timate goal of the fore­casts is spe­cified in terms of a stat­ist­ical func­tional such as the mean, a quantile, or a cer­tain risk meas­ure, the loss should in­centiv­ise truth­ful fore­casts in that the ex­pec­ted loss is strictly min­im­ised by the cor­rectly spe­cified fore­cast. If a func­tional pos­sesses such an in­cent­ive com­pat­ible loss func­tion, it is called eli­cit­able. Be­sides en­abling mean­ing­ful fore­cast com­par­ison, the eli­cit­ab­il­ity of a func­tional al­lows for M-es­tim­a­tions and re­gres­sion. Ac­know­ledging that there is a wealth of eli­cit­able func­tion­als (mean, quantiles, ex­pectiles) and non-eli­cit­able func­tion­als (vari­ance, Ex­pec­ted Short­fall), this talk ad­dresses aspects of the fol­low­ing Eli­cit­a­tion Prob­lem:
1) When is a func­tional eli­cit­able?
2) What is the class of in­cent­ive com­pat­ible loss func­tions?
3) What are dis­tin­guished loss func­tions to use in prac­tice?
4) How to cope with the non-eli­cit­ab­il­ity of a func­tional?
The em­phasis will lie on main achieve­ments for mul­tivari­ate func­tion­als such as the pair of risk meas­ures (Value-at-Risk, Ex­pec­ted Short­fall). It will also give an outlook to mod­ern and very re­cent achieve­ments in the realm of set-­val­ued func­tion­als which are suited to con­sider set-­val­ued meas­ures of sys­temic risk or con­fid­ence in­ter­vals and re­gions.

Kindly note that on Novem­ber 9 two talks are sched­uled at our in­sti­tute:
9:00 – 10:10  Nestor Pa­ro­lya (Leib­niz Uni­versity Han­nover)
11:00 – 12:10  To­bias Fissler (Im­per­ial Col­lege Lon­don)

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