Some topics in sequential density estimation

Let $X\sb1, X\sb2, \... X\sb{n}$ be i.i.d random variables with common unknown density function f. Here we are interested in estimating the unknown density f with bounded Mean Integrated Absolute Error (MIAE). Devroye and Gyorfi (1985) obtained asymptotic bounds for the MIAE in estimating f by a kernel estimate f\sb{n}. Using these bounds one can identify an appropriate sample size such that the MIAE is smaller than some pre-assigned quantity w $>$ 0. Hence there is no fixed sample size that can be used to solve the problem of bounding the MIAE. In this work we propose stopping rules and two-stage procedures for bounding the $L\sb1$ distance. We show that these procedures are asymptotically optimal in a certain sense as w $\to$ 0.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Kundu, Subrata

Contributors dc:contributor

• Martinsek, Adam T.

• Statistics

Statement dc:rights

• Copyright 1994 Kundu, Subrata

Language dc:language

eng

Identifier

AAI9503243
(UMI)AAI9503243

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/19231