Variance Inference Beyond the Sandwich for Asymptotically Linear Estimators with Second-Order Remainders
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914593235795968 |
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| author | Li, Lin Wu, Pengcheng |
| author_facet | Li, Lin Wu, Pengcheng |
| contents | Semiparametric estimators admitting a von Mises expansion often reduce inference to the influence-function variance. This reduction is justified when the second-order remainder is negligible in variance, a condition that is stronger than the usual product-rate requirement guaranteeing classical asymptotic linearity. When the remainder contributes non-negligible variance, the standard sandwich can underestimate the total sampling variance and Wald intervals can undercover; we call this the \emph{near-boundary regime}. We derive a finite-sample variance decomposition separating influence-function and remainder components, give a practical characterization of when sandwich variance can fail, and show that the leave-one-out jackknife and pairs cluster bootstrap can estimate the total variance under explicit regularity conditions. For the jackknife, consistency follows from a self-normalization argument; for the bootstrap, we work under a Mallows-2 consistency condition. An analytic expression for the amplification of the sandwich gap by intra-cluster correlation is derived for clustered data. A simulation study using a surrogate-assisted targeted learning estimator in stepped-wedge cluster-randomized trials illustrates the regime: the variance ratio $\hat{V}_{\rm JK}/\hat{V}_{\rm Sand}$ is 1.14--1.38 and persistent across cluster counts, and the refined procedures substantially improve coverage. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_14561 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Variance Inference Beyond the Sandwich for Asymptotically Linear Estimators with Second-Order Remainders Li, Lin Wu, Pengcheng Methodology Statistics Theory Semiparametric estimators admitting a von Mises expansion often reduce inference to the influence-function variance. This reduction is justified when the second-order remainder is negligible in variance, a condition that is stronger than the usual product-rate requirement guaranteeing classical asymptotic linearity. When the remainder contributes non-negligible variance, the standard sandwich can underestimate the total sampling variance and Wald intervals can undercover; we call this the \emph{near-boundary regime}. We derive a finite-sample variance decomposition separating influence-function and remainder components, give a practical characterization of when sandwich variance can fail, and show that the leave-one-out jackknife and pairs cluster bootstrap can estimate the total variance under explicit regularity conditions. For the jackknife, consistency follows from a self-normalization argument; for the bootstrap, we work under a Mallows-2 consistency condition. An analytic expression for the amplification of the sandwich gap by intra-cluster correlation is derived for clustered data. A simulation study using a surrogate-assisted targeted learning estimator in stepped-wedge cluster-randomized trials illustrates the regime: the variance ratio $\hat{V}_{\rm JK}/\hat{V}_{\rm Sand}$ is 1.14--1.38 and persistent across cluster counts, and the refined procedures substantially improve coverage. |
| title | Variance Inference Beyond the Sandwich for Asymptotically Linear Estimators with Second-Order Remainders |
| topic | Methodology Statistics Theory |
| url | https://arxiv.org/abs/2603.14561 |