Laws of the Iterated Logarithm for the Local U-Statistic Process

Evarist Giné () and David M. Mason ()
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Evarist Giné: University of Connecticut
David M. Mason: University of Delaware

Journal of Theoretical Probability, 2007, vol. 20, issue 3, 457-485

Abstract: Abstract Laws of the iterated logarithm are established for the local U-statistic process. This entails the development of probability inequalities and moment bounds for U-processes that should be of separate interest. The local U-statistic process is based upon an estimator of the density of a function of several i.i.d. variables proposed by Frees (J. Am. Stat. Assoc. 89, 517–525, 1994). As a consequence, our results are directly applicable to the derivation of exact rates of uniform in bandwidth consistency in the sup and in the L p norms for these estimators.

Keywords: U-Statistics; Law of iterated logarithm; Empirical process; Kernel density estimation (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10959-007-0067-0

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