Degree Type

Dissertation

Date of Award

2004

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Soumendra N. Lahiri

Abstract

In this work, we investigate consistency properties of normal approximation and block bootstrap approximations for sample quantiles of weakly dependent data. Under mild weak dependence conditions and mild smoothness conditions on the one-dimensional marginal distribution function, we show that the moving block bootstrap (MBB) method provides a valid approximation to the distribution of normalized sample quantile and the corresponding MBB estimator of the asymptotic variance is also strongly consistent. Along the line, we also examine the rate of convergence of the MBB approximation to the distribution of the sample quantile, and prove a Berry-Esseen Theorem, which indicates that the normal approximation to the distribution of the sample quantile under weak dependence is of order O(n-1/2).

DOI

https://doi.org/10.31274/rtd-180813-11028

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu

Copyright Owner

Shuxia Sun

Language

en

Proquest ID

AAI3145686

File Format

application/pdf

File Size

114 pages

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