About: Dvoretzky–Kiefer–Wolfowitz inequality

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In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved the inequality with an unspecified multiplicative constant C in front of the exponent on the right-hand side.

Attributes	Values
rdf:type	Thing yago:WikicatStatisticalInequalities yago:Abstraction100002137 yago:Attribute100024264 yago:Difference104748836 yago:Inequality104752221 yago:Quality104723816
rdfs:label	Dvoretzky–Kiefer–Wolfowitz inequality (en) Inégalité DKW (fr)
rdfs:comment	En probabilités et statistiques, l'inégalité DKW (Dvoretzky-Kiefer-Wolfowitz) précise à quel point la fonction de répartition empirique sera proche de la fonction de répartition théorique de la variable aléatoire étudiée. Cette inégalité est due aux mathématiciens Aryeh Dvoretzky, Jack Kiefer et Jacob Wolfowitz qui en 1956 ont prouvé l'inégalité mais avec une constante multiplicative indéterminée. Ce n'est qu'en 1990 que Pascal Massart montre que l'inégalité était vraie pour la constante , confirmant ainsi une conjecture de Birnbaum et McCarty. (fr) In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved the inequality with an unspecified multiplicative constant C in front of the exponent on the right-hand side. (en)
rdfs:seeAlso	CDF-based nonparametric confidence interval
foaf:depiction
dcterms:subject	Statistical inequalities Asymptotic theory (statistics) Empirical process
Wikipage page ID	8140616 (xsd:integer)
Wikipage revision ID	1108432944 (xsd:integer)
Link from a Wikipage to another Wikipage	Allan Birnbaum Statistical inequalities Uniform distribution (continuous) Empirical distribution function Concentration inequality Confidence and prediction bands Statistics Rate of convergence Cumulative distribution function Pascal Massart Glivenko–Cantelli theorem Kolmogorov–Smirnov test Probability Random variable Asymptotic theory (statistics) Jacob Wolfowitz Aryeh Dvoretzky Kaplan–Meier estimator Empirical process Random function Independent and identically distributed Jack Kiefer (mathematician)
sameAs	Dvoretzky–Kiefer–Wolfowitz inequality Dvoretzky–Kiefer–Wolfowitz inequality Dvoretzky–Kiefer–Wolfowitz inequality Dvoretzky–Kiefer–Wolfowitz inequality Dvoretzky–Kiefer–Wolfowitz inequality
dbp:wikiPageUsesTemplate	dbt:Reflist dbt:See_also dbt:Short_description
thumbnail	wiki-commons:Special:FilePath/DKW_bounds.svg?width=300
has abstract	In the theory of probability and statistics, the Dvoretzky–Kiefer–Wolfowitz–Massart inequality (DKW inequality) bounds how close an empirically determined distribution function will be to the distribution function from which the empirical samples are drawn. It is named after Aryeh Dvoretzky, Jack Kiefer, and Jacob Wolfowitz, who in 1956 proved the inequality with an unspecified multiplicative constant C in front of the exponent on the right-hand side. In 1990, Pascal Massart proved the inequality with the sharp constant C = 2, confirming a conjecture due to Birnbaum and McCarty. In 2021, Michael Naaman proved the multivariate version of the DKW inequality and generalized Massart's tightness result to the multivariate case, which results in a sharp constant of twice the number of variables, C = 2k. (en) En probabilités et statistiques, l'inégalité DKW (Dvoretzky-Kiefer-Wolfowitz) précise à quel point la fonction de répartition empirique sera proche de la fonction de répartition théorique de la variable aléatoire étudiée. Cette inégalité est due aux mathématiciens Aryeh Dvoretzky, Jack Kiefer et Jacob Wolfowitz qui en 1956 ont prouvé l'inégalité mais avec une constante multiplicative indéterminée. Ce n'est qu'en 1990 que Pascal Massart montre que l'inégalité était vraie pour la constante , confirmant ainsi une conjecture de Birnbaum et McCarty. (fr)
prov:wasDerivedFrom	wikipedia-en:Dvoretzky–Kiefer–Wolfowitz_inequality?oldid=1108432944&ns=0
page length (characters) of wiki page	9369 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Dvoretzky–Kiefer–Wolfowitz_inequality
is Link from a Wikipage to another Wikipage of	List of inequalities Empirical distribution function Pascal Massart Glivenko–Cantelli theorem List of New York University alumni Jack Kiefer (statistician) Jacob Wolfowitz Dvoretzky-Kiefer-Wolfowitz Inequality Dvoretzky-Kiefer-Wolfowitz inequality Aryeh Dvoretzky CDF-based nonparametric confidence interval List of statistics articles
is Wikipage redirect of	Dvoretzky-Kiefer-Wolfowitz Inequality Dvoretzky-Kiefer-Wolfowitz inequality
is known for of	Jacob Wolfowitz Aryeh Dvoretzky
is known for of	Jacob Wolfowitz Aryeh Dvoretzky
is foaf:primaryTopic of	wikipedia-en:Dvoretzky–Kiefer–Wolfowitz_inequality

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