Demystified: double robustness with nuisance parameters estimated at rate n-to-the-1/4
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910588683157504 |
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| author | Lok, Judith J. |
| author_facet | Lok, Judith J. |
| contents | Have you also been wondering what is this thing with double robustness and nuisance parameters estimated at rate n^(1/4)? It turns out that to understand this phenomenon one just needs the Middle Value Theorem (or a Taylor expansion) and some smoothness conditions. This note explains why under some fairly simple conditions, as long as the nuisance parameter theta in R^k is estimated at rate n^(1/4) or faster, 1. the resulting variance of the estimator of the parameter of interest psi in R^d does not depend on how the nuisance parameter theta is estimated, and 2. the sandwich estimator of the variance of psi-hat ignoring estimation of theta is consistent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02320 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Demystified: double robustness with nuisance parameters estimated at rate n-to-the-1/4 Lok, Judith J. Statistics Theory Have you also been wondering what is this thing with double robustness and nuisance parameters estimated at rate n^(1/4)? It turns out that to understand this phenomenon one just needs the Middle Value Theorem (or a Taylor expansion) and some smoothness conditions. This note explains why under some fairly simple conditions, as long as the nuisance parameter theta in R^k is estimated at rate n^(1/4) or faster, 1. the resulting variance of the estimator of the parameter of interest psi in R^d does not depend on how the nuisance parameter theta is estimated, and 2. the sandwich estimator of the variance of psi-hat ignoring estimation of theta is consistent. |
| title | Demystified: double robustness with nuisance parameters estimated at rate n-to-the-1/4 |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2409.02320 |