Markov Chain Marginal Bootstrap

Markov chain marginal bootstrap (MCMB) is a new method for constructing confidence intervals or regions for maximum likelihood estimators of certain parametric models and for a wide class of M estimators of linear regression. The MCMB method distinguishes itself from the usual bootstrap methods in two important aspects: it involves solving only one-dimensional equations for parameters of any dimension and produces a Markov chain rather than a (conditionally) independent sequence. It is designed to alleviate computational burdens often associated with bootstrap in high-dimensional problems. The validity of MCMB is established through asymptotic analyses and illustrated with empirical and simulation studies for linear regression and generalized linear models.