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| Natura: | Preprint |
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2026
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| Accesso online: | https://arxiv.org/abs/2601.13514 |
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| _version_ | 1866917211241709568 |
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| author | Perry, Ronan Panigrahi, Snigdha Witten, Daniela |
| author_facet | Perry, Ronan Panigrahi, Snigdha Witten, Daniela |
| contents | We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i) adding and subtracting carefully-constructed noise to a Gaussian random variable with unknown mean and known variance leads to two \emph{independent} Gaussian random variables; and (ii) both the selection event resulting from penalized M-estimation, and the event that a standard (non-selective) confidence interval for an M-estimator covers its target, can be characterized in terms of an approximately normal ``score variable". We combine these insights to show that -- when the noise is chosen carefully -- there is asymptotic independence between the model selected using a noisy penalized M-estimator, and the event that a standard (non-selective) confidence interval on noisy data covers the selected parameter. Therefore, selecting a model via penalized M-estimation (e.g. \verb=glmnet= in \verb=R=) on noisy data, and then conducting \emph{standard} inference on the selected model (e.g. \verb=glm= in \verb=R=) using noisy data, yields valid inference: \emph{no bespoke methods are required}. Our results require independence of the observations, but only weak distributional requirements. We apply the proposed approach to conduct inference on the association between sex and smoking in a social network. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13514 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Post-selection inference for penalized M-estimators via score thinning Perry, Ronan Panigrahi, Snigdha Witten, Daniela Methodology We consider inference for M-estimators after model selection using a sparsity-inducing penalty. While existing methods for this task require bespoke inference procedures, we propose a simpler approach, which relies on two insights: (i) adding and subtracting carefully-constructed noise to a Gaussian random variable with unknown mean and known variance leads to two \emph{independent} Gaussian random variables; and (ii) both the selection event resulting from penalized M-estimation, and the event that a standard (non-selective) confidence interval for an M-estimator covers its target, can be characterized in terms of an approximately normal ``score variable". We combine these insights to show that -- when the noise is chosen carefully -- there is asymptotic independence between the model selected using a noisy penalized M-estimator, and the event that a standard (non-selective) confidence interval on noisy data covers the selected parameter. Therefore, selecting a model via penalized M-estimation (e.g. \verb=glmnet= in \verb=R=) on noisy data, and then conducting \emph{standard} inference on the selected model (e.g. \verb=glm= in \verb=R=) using noisy data, yields valid inference: \emph{no bespoke methods are required}. Our results require independence of the observations, but only weak distributional requirements. We apply the proposed approach to conduct inference on the association between sex and smoking in a social network. |
| title | Post-selection inference for penalized M-estimators via score thinning |
| topic | Methodology |
| url | https://arxiv.org/abs/2601.13514 |