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  • Kniha je prvním souborným dílem o singularitách lineárních statistických modelů a měla by být východiskem pro další výzkum v oblasti matematické statistiky a její aplikace. Pozornost je soustředěna zejména na problémy teorie odhadu, oblastí spolehlivosti a testování hypotéz ve třech základních strukturách lineárních modelů. Jedná se o modely bez podmínek na parametry střední hodnoty vektoru měření, o modely, kdy parametry střední hodnoty jsou vázané lineárními podmínkami a o modely, kdy se v podmínkách objevují další parametry. Text obsahuje názorné příklady, které kromě ilustrace teorie ukazují, že řada praktických úloh může vést k singularitám. Kniha je doplněna podrobným dodatkem obsahujícím poznatky z maticové algebry a teorie pravděpodobnosti. (cs)
  • The book presents a first comprehensive treatment on singularities in linear statistical models and is intended as a point of departure for further research in mathematical statistics and its applications. The focus is centered on problems in estimation theory, confidence regions and hypothesis testing in three basic structures of linear models. These are: models without constraints on mean-value parameters of an observation vector; models with linear constraints on mean-value parameters; and models with additional parameters in the constraints. Illustrative examples complement the theory, showing that many practical problems can lead to singularities. The book includes detailed Appendix on matrix algebra and probability theory.
  • The book presents a first comprehensive treatment on singularities in linear statistical models and is intended as a point of departure for further research in mathematical statistics and its applications. The focus is centered on problems in estimation theory, confidence regions and hypothesis testing in three basic structures of linear models. These are: models without constraints on mean-value parameters of an observation vector; models with linear constraints on mean-value parameters; and models with additional parameters in the constraints. Illustrative examples complement the theory, showing that many practical problems can lead to singularities. The book includes detailed Appendix on matrix algebra and probability theory. (en)
Title
  • Linear statistical models: Regularity and singularities
  • Linear statistical models: Regularity and singularities (en)
  • Lineární statistické modely: regularity a singularity (cs)
skos:prefLabel
  • Linear statistical models: Regularity and singularities
  • Linear statistical models: Regularity and singularities (en)
  • Lineární statistické modely: regularity a singularity (cs)
skos:notation
  • RIV/61989592:15310/07:00004752!RIV08-MSM-15310___
http://linked.open...avai/riv/aktivita
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  • Z(MSM6198959214)
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  • 431124
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  • RIV/61989592:15310/07:00004752
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  • statistical models; singularities; estimation theory; reliability theory; statistical hypothesis testing (en)
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  • [91C4BE303427]
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  • Praha
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  • Linear statistical models: Regularity and singularities
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...v/pocetStranKnihy
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http://linked.open...iv/tvurceVysledku
  • Kubáček, Lubomír
  • Fišerová, Eva
  • Kunderová, Pavla
http://linked.open...n/vavai/riv/zamer
number of pages
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  • Academia
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  • 978-80-200-1562-4
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  • 15310
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