Stabilized Cross-Validation of Smoothness in Density Deconvolution
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916911523037184 |
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| author | Kent, David |
| author_facet | Kent, David |
| contents | We consider density estimation under measurement error with the Smoothness-Penalized Deconvolution (SPeD) estimator. The estimator has a tuning parameter regulating the smoothness of the estimate, and proper choice of this parameter is critical for forming good estimates. We derive the cross-validation choice of tuning parameter for the SPeD estimator, but it performs very poorly. We introduce a stabilized cross-validation (SCV) criterion which unbiasedly estimates the mean integrated squared error (MISE) for a smaller sample size, and use asymptotic arguments to obtain an appropriate tuning parameter from this stabilized criterion. We show that the SCV is a strongly consistent estimator of the MISE, and that it is the minimum variance unbiased estimator of the MISE. In a simulation study, we show that the SCV approach outperforms the previously recommended choice of tuning parameter in nearly all settings, and in a majority of the settings, SPeD with the SCV outperforms the classic deconvoluting kernel estimator with its recommended choice of tuning parameter. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01478 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stabilized Cross-Validation of Smoothness in Density Deconvolution Kent, David Statistics Theory We consider density estimation under measurement error with the Smoothness-Penalized Deconvolution (SPeD) estimator. The estimator has a tuning parameter regulating the smoothness of the estimate, and proper choice of this parameter is critical for forming good estimates. We derive the cross-validation choice of tuning parameter for the SPeD estimator, but it performs very poorly. We introduce a stabilized cross-validation (SCV) criterion which unbiasedly estimates the mean integrated squared error (MISE) for a smaller sample size, and use asymptotic arguments to obtain an appropriate tuning parameter from this stabilized criterion. We show that the SCV is a strongly consistent estimator of the MISE, and that it is the minimum variance unbiased estimator of the MISE. In a simulation study, we show that the SCV approach outperforms the previously recommended choice of tuning parameter in nearly all settings, and in a majority of the settings, SPeD with the SCV outperforms the classic deconvoluting kernel estimator with its recommended choice of tuning parameter. |
| title | Stabilized Cross-Validation of Smoothness in Density Deconvolution |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2401.01478 |