2019/08/11 by Eli S. Kravitz, Kravitz, Eli S., Raymond J. Carroll +3 · 1 citation
Decision Sciences · Mathematics · #Advanced Statistical Process Monitoring #Applied mathematics #Asymptotic distribution #Confidence interval #Estimating equations #Estimation theory #Estimator #FOS: Computer and information sciences #Geometry #Mathematics #Methodology (stat.ME) #Parametric equation #Parametric statistics #Physics #Sample (material) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical hypothesis testing #Statistics #stat.ME
paper · pdf · doi:10.48550/arxiv.1908.03968
published in arXiv (Cornell University) (Cornell University) · preprint. arXiv admin note: text overlap with arXiv:1908.03967
arxiv created 2019/08/11 · openalex publication_date 2019/08/11 · arxiv updated 2019/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose there are two unknown parameters, each parameter is the solution to an estimating equation, and the estimating equation of one parameter depends on the other parameter. The parameters can be jointly estimated by "stacking" their estimating equations and solving for both parameters simultaneously. Asymptotic confidence intervals are readily available for stacked estimating equations. We introduce a bootstrap-based hypothesis test for stacked estimating equations which does not rely on asymptotic approximations. Test statistics are constructed by splitting the sample in two, estimating the first parameter on a portion of the sample then plugging the result into the second estimating equation to solve for the next parameter using the remaining sample. To reduce simulation variability from a single split, we repeatedly split the sample and take the sample mean of all the estimates. For parametric models, we derive the limiting distribution of sample splitting estimator and show they are equivalent to stacked estimating equations.