.png){kind=icon}
.png){kind=icon}
Return
BOOTSTRAP CONFIDENCE SETS UNDER MODEL MISSPECIFICATION
.png){kind=icon}
OA
AI
DOI：10.1214/15-AOS1355.png)
.png){kind=icon}
.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
A multiplier bootstrap procedure for construction of likelihood-based confidence sets is considered for finite samples and a possible model misspecification. Theoretical results justify the bootstrap validity for a small or moderate sample size and allow to control the impact of the parameter dimension p: the bootstrap approximation works if p(3)/n is small. The main result about bootstrap validity continues to apply even if the underlying parametric model is misspecified under the so-called small modelling bias condition. In the case when the true model deviates significantly from the considered parametric family, the bootstrap procedure is still applicable but it becomes a bit conservative: the size of the constructed confidence sets is increased by the modelling bias. We illustrate the results with numerical examples for misspecified linear and logistic regressions.
Keywords:
Likelihood-based bootstrap confidence set
finite sample size
multiplier/weighted bootstrap
Gaussian approximation
Pinsker's inequality
AI Summary
Key information extracted from the uploaded paper, including a brief overview, abstract, background, key highlights, visual analysis, and future outlook.