Asymptotic coverage probabilities of bootstrap percentile confidence intervals for constrained parameters

12/07/2017
by   Chunlin Wang, et al.
0

The asymptotic behaviour of the commonly used bootstrap percentile confidence interval is investigated when the parameters are subject to linear inequality constraints. We concentrate on the important one- and two-sample problems with data generated from general parametric distributions in the natural exponential family. The focus of this paper is on quantifying the coverage probabilities of the parametric bootstrap percentile confidence intervals, in particular their limiting behaviour near boundaries. We propose a local asymptotic framework to study this subtle coverage behaviour. Under this framework, we discover that when the true parameters are on, or close to, the restriction boundary, the asymptotic coverage probabilities can always exceed the nominal level in the one-sample case; however, they can be, remarkably, both under and over the nominal level in the two-sample case. Using illustrative examples, we show that the results provide theoretical justification and guidance on applying the bootstrap percentile method to constrained inference problems.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
01/26/2022

Confidence Intervals for the Generalisation Error of Random Forests

Out-of-bag error is commonly used as an estimate of generalisation error...
research
05/19/2020

Bootstrap prediction intervals with asymptotic conditional validity and unconditional guarantees

Focus on linear regression model, in this paper we introduce a bootstrap...
research
08/24/2018

Applications of the Fractional-Random-Weight Bootstrap

The bootstrap, based on resampling, has, for several decades, been a wid...
research
05/16/2019

Non-Asymptotic Inference in a Class of Optimization Problems

This paper describes a method for carrying out non-asymptotic inference ...
research
08/08/2017

Exponential Random Graph Models with Big Networks: Maximum Pseudolikelihood Estimation and the Parametric Bootstrap

With the growth of interest in network data across fields, the Exponenti...
research
03/06/2023

Differentially Private Confidence Interval for Extrema of Parameters

This paper aims to construct a valid and efficient confidence interval f...
research
04/21/2022

New confidence interval methods for Shannon index

Several factors affect the structure of communities, including biologica...

Please sign up or login with your details

Forgot password? Click here to reset