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Description
  • Pro standatní exponenciální rodinu, nebo její kanonicky konvexní podrodinu, je zaveden zobecněný maximálně věrohodný odhad. Je to rozšíření zobrazení, které přiřazuje empirické střední hodnotě výběru, pro kterou maximalizátor t* z R^d odpovídající věrohodnostní funkce existuje, tu pravděpodobnostní míru z rodiny, která má parameter t*. Toto rozšíření přiřazuje každému vektoru a z R^d, pro které je věrohodnostní funkce omezená zhora, nějakou pravděpodobnostní míru z uzávěru rodiny vzhledem ke varianční vzdálenosti. Toto rozšíření je podrobně popsáno, zvlástě jeho definiční obor a obor hodnot, a to bez předpokladů regularity. (cs)
  • For a standard full exponential family on R^d, or its canonically convex subfamily, the generalized maximum likelihood estimator is an extension of the mapping that assigns to the mean a from R^d of a sample for which a maximizer t^* of a corresponding likelihood function exists, the member of the family parameterized by t^*. This extension assigns to each a from /R^d with the likelihood function bounded above, a member of the closure of the family in variation distance. Its detailed description, complete characterization of domain and range, and additional results are presented, not imposing any regularity assumptions. In addition to basic convex analysis tools, the authors' prior results on convex cores of measures and closures of exponential families are used.
  • For a standard full exponential family on R^d, or its canonically convex subfamily, the generalized maximum likelihood estimator is an extension of the mapping that assigns to the mean a from R^d of a sample for which a maximizer t^* of a corresponding likelihood function exists, the member of the family parameterized by t^*. This extension assigns to each a from /R^d with the likelihood function bounded above, a member of the closure of the family in variation distance. Its detailed description, complete characterization of domain and range, and additional results are presented, not imposing any regularity assumptions. In addition to basic convex analysis tools, the authors' prior results on convex cores of measures and closures of exponential families are used. (en)
Title
  • Generalized maximum likelihood estimates for exponential families
  • Generalized maximum likelihood estimates for exponential families (en)
  • Zobecněné maximálně věrohodné odhady pro exponenciální rodiny (cs)
skos:prefLabel
  • Generalized maximum likelihood estimates for exponential families
  • Generalized maximum likelihood estimates for exponential families (en)
  • Zobecněné maximálně věrohodné odhady pro exponenciální rodiny (cs)
skos:notation
  • RIV/67985556:_____/08:00311133!RIV09-AV0-67985556
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(IAA100750603), Z(AV0Z10750506)
http://linked.open...iv/cisloPeriodika
  • 1-2
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 369056
http://linked.open...ai/riv/idVysledku
  • RIV/67985556:_____/08:00311133
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • accessible face; convex core; exponential family; information divergence; partial mean; variation distance closure; log-convexity; maximum likelihood (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • DE - Spolková republika Německo
http://linked.open...ontrolniKodProRIV
  • [9C71AC3F396B]
http://linked.open...i/riv/nazevZdroje
  • Probability Theory and Related Fields
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 141
http://linked.open...iv/tvurceVysledku
  • Matúš, František
  • Csiszár, I.
http://linked.open...ain/vavai/riv/wos
  • 000252807600008
http://linked.open...n/vavai/riv/zamer
issn
  • 0178-8051
number of pages
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