Bahadur-Kiefer theorems for the product-limit process
نویسندگان
چکیده
منابع مشابه
An Lp-view of the Bahadur-Kiefer Theorem
Let αn and βn be respectively the uniform empirical and quantile processes, and define Rn = αn + βn, which usually is referred to as the Bahadur–Kiefer process. The well-known Bahadur–Kiefer theorem confirms the following remarkable equivalence: ‖Rn‖/ √ ‖αn‖ ∼ n−1/4(log n) almost surely, as n goes to infinity, where ‖f‖ = sup0≤t≤1 |f(t)| is the L∞-norm. We prove that ‖Rn‖2/ √ ‖αn‖1 ∼ n−1/4 almo...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1990
ISSN: 0047-259X
DOI: 10.1016/0047-259x(90)90029-h