Extensions of Markov Chain Marginal Bootstrap

The Markov chain marginal bootstrap (MCMB) is a new bootstrap method proposed by He and Hu (2002) for constructing confidence intervals or regions based on likelihood equations. It is designed to ease the computational burden of bootstrap in high-dimensional problems. It differs from the usual bootstrap methods in two aspects: a set of p one-dimensional equations is solved in place of a p-dimensional system of equations for each bootstrap estimate of the parameter; the resulting estimates form a Markov chain rather than an independent sequence of realizations. This thesis proposes two modifications to extend the use of MCMB to more general models and estimators. The first modification is a transformation of the parameter space, which reduces high autocorrelation of the resulting MCMB chains, and improves on the efficiency and stability of the procedure. The second is a transformation of the estimating equations, which extends the use of MCMB beyond the likelihood-based estimators. Through examples and Monte Carlo simulations, the transformations proposed in this thesis are shown to be valuable and sometimes necessary for successful applications of MCMB to linear and nonlinear models.

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

2015

Author dc:creator

• Kocherginsky, Maria Nikolai

Contributors dc:contributor

• He, Xuming

• Statistics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3086103

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87395