The L1-norm density estimator process

• 成果类型: Article
• 署名作者: Giné, E; Mason, DM; Zaitsev, AY
• 署名单位: University of Connecticut; University of Delaware; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences; St. Petersburg Department of the Steklov Mathematical Institute of the Russian Academy of Sciences
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 719-768
• 关键词: central limit-theorem; Asymptotic Normality; Empirical Processes; random-variables; random vectors; lp-norms; inequalities; CONVERGENCE

摘要

The notion of an L-1-norm density estimator process indexed by a class of kernels is introduced. Then a functional central limit theorem and a Glivenko-Cantelli theorem are established for this process. While assembling the necessary machinery to prove these results, a body of Poissonization techniques and restricted chaining methods is developed, which is useful for studying weak convergence of general processes indexed by a class of functions. None of the theorems imposes any condition at all on the underlying Lebesgue density f. Also, somewhat unexpectedly, the distribution of the limiting Gaussian process does not depend on f.