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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2408.16763 |
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| _version_ | 1866929478671794176 |
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| author | Jiang, Yiran Liu, Chuanhai Zhang, Heping |
| author_facet | Jiang, Yiran Liu, Chuanhai Zhang, Heping |
| contents | While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed $\textit{calibrated bootstrap}$, designed to generate finite sample-valid parametric inference from a sample of size $n$. The central idea is to calibrate an $m$-out-of-$n$ resampling scheme, where the calibration parameter $m$ is determined against inferential pivotal quantities derived from the cumulative distribution functions of loss functions in parameter estimation. The method comprises two algorithms. The first, named $\textit{resampling approximation}$ (RA), employs a $\textit{stochastic approximation}$ algorithm to find the value of the calibration parameter $m=m_α$ for a given $α$ in a manner that ensures the resulting $m$-out-of-$n$ bootstrapped $1-α$ confidence set is valid. The second algorithm, termed $\textit{distributional resampling}$ (DR), is developed to further select samples of bootstrapped estimates from the RA step when constructing $1-α$ confidence sets for a range of $α$ values is of interest. The proposed method is illustrated and compared to existing methods using linear regression with and without $L_1$ penalty, within the context of a high-dimensional setting and a real-world data application. The paper concludes with remarks on a few open problems worthy of consideration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_16763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite Sample Valid Inference via Calibrated Bootstrap Jiang, Yiran Liu, Chuanhai Zhang, Heping Methodology Computation While widely used as a general method for uncertainty quantification, the bootstrap method encounters difficulties that raise concerns about its validity in practical applications. This paper introduces a new resampling-based method, termed $\textit{calibrated bootstrap}$, designed to generate finite sample-valid parametric inference from a sample of size $n$. The central idea is to calibrate an $m$-out-of-$n$ resampling scheme, where the calibration parameter $m$ is determined against inferential pivotal quantities derived from the cumulative distribution functions of loss functions in parameter estimation. The method comprises two algorithms. The first, named $\textit{resampling approximation}$ (RA), employs a $\textit{stochastic approximation}$ algorithm to find the value of the calibration parameter $m=m_α$ for a given $α$ in a manner that ensures the resulting $m$-out-of-$n$ bootstrapped $1-α$ confidence set is valid. The second algorithm, termed $\textit{distributional resampling}$ (DR), is developed to further select samples of bootstrapped estimates from the RA step when constructing $1-α$ confidence sets for a range of $α$ values is of interest. The proposed method is illustrated and compared to existing methods using linear regression with and without $L_1$ penalty, within the context of a high-dimensional setting and a real-world data application. The paper concludes with remarks on a few open problems worthy of consideration. |
| title | Finite Sample Valid Inference via Calibrated Bootstrap |
| topic | Methodology Computation |
| url | https://arxiv.org/abs/2408.16763 |