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Hajek–Renyi-type inequality for associated sequences

✍ Scribed by B.L.S. Prakasa Rao

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
86 KB
Volume
57
Category
Article
ISSN
0167-7152

No coin nor oath required. For personal study only.

✦ Synopsis

Let { ; F; P} be a probability space and {X n ; n ¿ 1} be a sequence of random variables deÿned on it. A ÿnite sequence {X 1 ; : : : ; X n } is said to be associated if for any two component wise non-decreasing functions f and g on R n ; Cov(f(X 1 ; : : : ; X n ); g(X 1 ; : : : ; X n )) ¿ 0. A Hajek-Renyi-type inequality for associated sequences is proved. Some applications are given.

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Professor Lajos Horvà ath has pointed out that the names Hà ajeck-R enyi (resp. H ajeck-R enyi) are misspellings in the title and the text of the above-mentioned article. As already corrected above the correct spelling is: Hà ajek-Rà enyi.