Abstract The Markov chain marginal bootstrap (MCMB) was introduced by He and Hu [2002. Markov chain marginal bootstrap. J. Amer. Statist. Assoc. 97(459) (2002) 783–795] as a bootstrap-based method for constructing confidence intervals or regions for a wide class of M-estimators in linear regression and maximum likelihood estimators in certain parametric models. In this article we discuss more general applications of MCMB- A , an extension of the MCMB algorithm, which was first proposed in Kocherginsky et al. [2005. Practical confidence intervals for regression quantiles. J. Comput. Graphical Statist. 14, 41–55] for quantile regression models. We also present a further extension of the MCMB algorithm, the B -transformation, which is a transformation of the estimating equations, aiming to broaden the applicability of the MCMB algorithm to general estimating equations that are not necessarily likelihood-based. We show that applying the A - and B -transformations jointly enables the MCMB algorithm to be used for inference related to a very general class of estimating equations. We illustrate the use of the MCMB- AB algorithm with a nonlinear regression model with heteroscedastic error distribution.
[1]
M. D. J. Gamero,et al.
Reduced bootstrap for the median
,
2004
.
[2]
G. J. Babu,et al.
A Note on Bootstrapping the Sample Median
,
1984
.
[3]
R. Tibshirani,et al.
An Introduction to the Bootstrap
,
1995
.
[4]
Anthony C. Davison,et al.
Bootstrap Methods and Their Application
,
1998
.
[5]
Feifang Hu,et al.
Markov Chain Marginal Bootstrap
,
2002
.
[6]
J. Zidek,et al.
A bootstrap based on the estimating equations of the linear model
,
1995
.
[7]
P. J. Huber.
Robust Estimation of a Location Parameter
,
1964
.
[8]
Xuming He,et al.
Practical Confidence Intervals for Regression Quantiles
,
2005
.
[9]
Douglas M. Bates,et al.
Nonlinear Regression Analysis and Its Applications
,
1988
.