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University of Illinois at Urbana-Champaign
Some Limit Theorems (Empirical Processes)
Abstract
dc:descriptionWe establish a central limit theorem and bounded and compact laws of the iterated logarithm for partial sum processes indexed by classes of functions. For the central limit theorem, we assume an envelope condition and a majorizing measure condition more general than the usual metric entropy with bracketing. For the laws of the iterated logarithm, we assume an envelope condition and a growth condition on the metric entropy under bracketing. Examples show that our results are sharp. As a corollary we obtain new results for weighted sums of independent identically distributed random variables.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Dissertation
- Discipline thesis:degree_discipline
- Mathematics
- Grantor
- University of Illinois at Urbana-Champaign
- Year dc:date
- 2014
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Lacey, Michael Thoreau
Subjects
dc:subject × 1Identifiers
dc:identifier.*- Identifier
- (UMI)AAI8721684
- OAI identifier oai:identifier
- oai:www.ideals.illinois.edu:2142/71257