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https://hdl.handle.net/2142/87395
Description
Title
Extensions of Markov Chain Marginal Bootstrap
Author(s)
Kocherginsky, Maria Nikolai
Issue Date
2003
Doctoral Committee Chair(s)
He, Xuming
Department of Study
Statistics
Discipline
Statistics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Language
eng
Abstract
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.
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