Laws of the Iterated Logarithm for the Local U–statistic Process
نویسندگان
چکیده
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 (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 Lp norms for these estimators. Short title: Local U–statistic process LIL AMS 2000 Subject Classifications: 60F05, 60F15, 62E20, 62G30.
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