Geodesic
A Bahadur--Kiefer law for the Nadaraya empiric-quantile processes
Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 380-392

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We study the a.s. behavior of Nadaraya's empiric-quantile processes $\widehat{R}_{n}(\,\cdot\,)$. Proceeding by invariance we exploit stochastic properties of $\|\widehat{R}_{n}\|$ and show that a Bahadur–Kiefer strong law holds for these processes demonstrating robustness with respect to the class of perturbed kernel empirical d.f.'s. Also, in the process of obtaining our result, we derive a Strassen-type law of the iterated logarithm which extends a theorem of Finkelstein and is likely to be of independent interest. In addition, a brief profile of applications is included.
Keywords: Bahadur–Kiefer law, Strassen-type law of the iterated logarithm.
Mots-clés : perturbed kernel empiric-quantile processes 
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     title = {A {Bahadur--Kiefer} law for the {Nadaraya} empiric-quantile processes},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     language = {en},
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S. S. Ralescu. A Bahadur--Kiefer law for the Nadaraya empiric-quantile processes. Teoriâ veroâtnostej i ee primeneniâ, Tome 41 (1996) no. 2, pp. 380-392. http://geodesic.mathdoc.fr/item/TVP_1996_41_2_a9/