Almost sure behavior for increments of U-statistics

Beschreibung der Fluktuation von Zuwächsen für U-Statistiken

by Mohammed Abujarad
Doctoral thesis
Date of Examination:2007-01-18
Date of issue:2007-10-09
Advisor:Prof. Dr. Manfred Denker
Referee:Prof. Dr. Manfred Denker
Referee:Prof. Dr. Susanne Koch
Referee:Prof. Dr. Gert Lube
Persistent Address: http://dx.doi.org/10.53846/goediss-2486

 

 

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Abstract

English

This thesis is concerned with a new type of almost sure behavior which was introduced by Erdös and Renyi. They found that the maxima of partial sums of independent and identically distributed random variables summed over blocks of length r(n) converge almost surely after appropriate norming to some non-zero value. This value strongly depends on the growth rate of r(n) and is determined by the Laplace transform of the distribution. For a nondecreasing sequence of natural numbers we introduce two different types of statistics based on increments of U-statistics of degree m. We extended Erdös-Renyi and Shepp laws as well as Csögö Revez law for U-statistics.
Keywords: Erdös-Renyi Law for U-statistics

Other Languages

Diese Dissertation beschäftigt sich mit Erdös-Renyi und Shepp Gesetze sowie Csörgö-Revez Gesetz für unabhängiger, identische verteilter zufälliger Größen. Wir beweisen Erdös-Renyi und Shepp Gesetze sowie Csörgö-Revez Gesetz für U- Statistiken.
Schlagwörter: Erdös-Renyi Gesetz für U-Statistiken
 
Statistik