. "32"^^ . "Csisz\u00E1r, I." . "369056" . "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 . . "[9C71AC3F396B]" . "DE - Spolkov\u00E1 republika N\u011Bmecko" . . . . . "0178-8051" . . "Zobecn\u011Bn\u00E9 maxim\u00E1ln\u011B v\u011Brohodn\u00E9 odhady pro exponenci\u00E1ln\u00ED rodiny"@cs . . "RIV/67985556:_____/08:00311133" . "Probability Theory and Related Fields" . "141" . "Pro standatn\u00ED exponenci\u00E1ln\u00ED rodinu, nebo jej\u00ED kanonicky konvexn\u00ED podrodinu, je zaveden zobecn\u011Bn\u00FD maxim\u00E1ln\u011B v\u011Brohodn\u00FD odhad. Je to roz\u0161\u00ED\u0159en\u00ED zobrazen\u00ED, kter\u00E9 p\u0159i\u0159azuje empirick\u00E9 st\u0159edn\u00ED hodnot\u011B v\u00FDb\u011Bru, pro kterou maximaliz\u00E1tor t* z R^d odpov\u00EDdaj\u00EDc\u00ED v\u011Brohodnostn\u00ED funkce existuje, tu pravd\u011Bpodobnostn\u00ED m\u00EDru z rodiny, kter\u00E1 m\u00E1 parameter t*. Toto roz\u0161\u00ED\u0159en\u00ED p\u0159i\u0159azuje ka\u017Ed\u00E9mu vektoru a z R^d, pro kter\u00E9 je v\u011Brohodnostn\u00ED funkce omezen\u00E1 zhora, n\u011Bjakou pravd\u011Bpodobnostn\u00ED m\u00EDru z uz\u00E1v\u011Bru rodiny vzhledem ke varian\u010Dn\u00ED vzd\u00E1lenosti. Toto roz\u0161\u00ED\u0159en\u00ED je podrobn\u011B pops\u00E1no, zvl\u00E1st\u011B jeho defini\u010Dn\u00ED obor a obor hodnot, a to bez p\u0159edpoklad\u016F regularity."@cs . "RIV/67985556:_____/08:00311133!RIV09-AV0-67985556" . . . . "2"^^ . "P(IAA100750603), Z(AV0Z10750506)" . "Generalized maximum likelihood estimates for exponential families" . "1"^^ . . . . . "Generalized maximum likelihood estimates for exponential families" . "Generalized maximum likelihood estimates for exponential families"@en . . . "000252807600008" . . "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." . "accessible face; convex core; exponential family; information divergence; partial mean; variation distance closure; log-convexity; maximum likelihood"@en . "Mat\u00FA\u0161, Franti\u0161ek" . "Zobecn\u011Bn\u00E9 maxim\u00E1ln\u011B v\u011Brohodn\u00E9 odhady pro exponenci\u00E1ln\u00ED rodiny"@cs . . "Generalized maximum likelihood estimates for exponential families"@en . "1-2" . . . .