Maximal Inequalities for Degenerate $U$-Processes with Applications to Optimization Estimators
Maximal Inequalities for Degenerate $U$-Processes with Applications to Optimization Estimators
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DOI：
10.1214/aos/1176325377
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发表时间：
1994-03
影响因子：
4.5
通讯作者：
R. Sherman
中科院分区：
文献类型：
--
作者：
R. Sherman
建立了k阶退化U-过程的极大不等式，k ≥ 1.结果依赖于k阶形式的矩不等式（由于Bonami（1970）），以及来自经验过程理论的链式和对称化不等式的扩展。一致收敛速度。极大值不等式可用于确定优化具有U-过程结构的准则函数的估计量的极限分布。作为应用，证明了最大化一个三阶U过程的半参数回归估计量是渐近正态分布的，且是相合的。
Maximal Inequalities for degenerate U-processes of order k, k ≥ 1, are established. The results rest on a moment inequality (due to Bonami (1970)) for kth-order forms, and extensions of chaining and symmetrization inequalities from the theory of empirical processes. Rates of uniform convergence are obtained. The maximal inequalities can be used to determine the limiting distribution of estimators that optimize criterion functions having U-process structure. As an application, a semiparametric regression estimator that maximizes a U-process of order three is shown to be √ n-consistent and asymptotically normally distributed.