Two-Point Dependent Wild Bootstrap for Weakly Dependent Estimating Equations
Abstract
This paper develops a general two-point dependent wild bootstrap (DWB) for weakly dependent estimating equations. Its key feature is that the two-point marginal distribution and the latent serial dependence specification can be chosen separately. The construction combines a normalized two-point distribution with a stationary latent Gaussian process via a Gaussian copula transformation, includes dependent Rademacher and Mammen multipliers, and nests the classical iid two-point wild bootstrap as the serially independent case. The induced multiplier autocovariances determine the lag weights in a corresponding heteroskedasticity- and autocorrelation-consistent (HAC) covariance estimator, which coincides exactly with the conditional covariance of the bootstrap estimating-equation sum. We establish first-order bootstrap validity for asymptotically linear estimators by showing that the matched-HAC estimator consistently estimates the long-run covariance and that the bootstrap estimating-equation sum converges conditionally to the same Gaussian limit as its original-sample counterpart, yielding valid HAC-studentized z-tests and the corresponding Wald and Lagrange multiplier tests. Monte Carlo experiments in nonlinear generalized method of moments (GMM) and linear regression, with common HAC studentization and matched multiplier covariances, show that dependent Rademacher generally yields better size control than Mammen and Gaussian DWB, especially for restricted z-tests. An application illustrates differences between asymptotic and bootstrap inference.
Related
- Limit theory for a class of non-stationary linear processes with weakly dependent heavy-tailed innovations
- Stein's functional method for weakly dependent random variables
- Optimal CLT error bounds in the second order Wasserstein metric via Stein's method for weakly dependent sequences
- Coupled unbiased MCMC for estimating Shapley effects under dependent inputs
- Uniform Gaussian Approximation for The Quasi-Likelihood Estimator for a Weakly Dependent Nonlinear Time Series Models
BibTeX
@misc{nishi2026twopoint,
title = {{Two-Point Dependent Wild Bootstrap for Weakly Dependent Estimating Equations}},
author = {Mikihito Nishi and Takashi Yamagata},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.32369},
eprint = {2609.32369},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32369},
}
RIS
TY - UNPB
TI - Two-Point Dependent Wild Bootstrap for Weakly Dependent Estimating Equations
AU - Mikihito Nishi
AU - Takashi Yamagata
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2609.32369
UR - https://arxiv.org/abs/2609.32369
AB - This paper develops a general two-point dependent wild bootstrap (DWB) for weakly dependent estimating equations. Its key feature is that the two-point marginal distribution and the latent serial dependence specification can be chosen separately. The construction combines a normalized two-point distribution with a stationary latent Gaussian process via a Gaussian copula transformation, includes dependent Rademacher and Mammen multipliers, and nests the classical iid two-point wild bootstrap as the serially independent case. The induced multiplier autocovariances determine the lag weights in a corresponding heteroskedasticity- and autocorrelation-consistent (HAC) covariance estimator, which coincides exactly with the conditional covariance of the bootstrap estimating-equation sum. We establish first-order bootstrap validity for asymptotically linear estimators by showing that the matched-HAC estimator consistently estimates the long-run covariance and that the bootstrap estimating-equation sum converges conditionally to the same Gaussian limit as its original-sample counterpart, yielding valid HAC-studentized z-tests and the corresponding Wald and Lagrange multiplier tests. Monte Carlo experiments in nonlinear generalized method of moments (GMM) and linear regression, with common HAC studentization and matched multiplier covariances, show that dependent Rademacher generally yields better size control than Mammen and Gaussian DWB, especially for restricted z-tests. An application illustrates differences between asymptotic and bootstrap inference.
ER -