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Abstract We propose a new procedure for inference on optimal treatment regimes in the model‐free setting, which does not require to specify an outcome regression model. Existing model‐free estimators for optimal treatment regimes are usually not suitable for the purpose of inference, because they either have nonstandard asymptotic distributions or do not necessarily guarantee consistent estimation of the parameter indexing the Bayes rule due to the use of surrogate loss. We first study a smoothed robust estimator that directly targets the parameter corresponding to the Bayes decision rule for optimal treatment regimes estimation. This estimator is shown to have an asymptotic normal distribution. Furthermore, we verify that a resampling procedure provides asymptotically accurate inference for both the parameter indexing the optimal treatment regime and the optimal value function. A new algorithm is developed to calculate the proposed estimator with substantially improved speed and stability. Numerical results demonstrate the satisfactory performance of the new methods.
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High‐dimensional robust inference for Cox regression models using desparsified Lasso
Abstract We consider high‐dimensional inference for potentially misspecified Cox proportional hazard models based on low‐dimensional results by Lin and Wei (1989). A desparsified Lasso estimator is proposed based on the log partial likelihood function and shown to converge to a pseudo‐true parameter vector. Interestingly, the sparsity of the true parameter can be inferred from that of the above limiting parameter. Moreover, each component of the above (nonsparse) estimator is shown to be asymptotically normal with a variance that can be consistently estimated even under model misspecifications. In some cases, this asymptotic distribution leads to valid statistical inference procedures, whose empirical performances are illustrated through numerical examples.
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- Award ID(s):
- 1830392
- PAR ID:
- 10449921
- Publisher / Repository:
- Wiley-Blackwell
- Date Published:
- Journal Name:
- Scandinavian Journal of Statistics
- Volume:
- 48
- Issue:
- 3
- ISSN:
- 0303-6898
- Page Range / eLocation ID:
- p. 1068-1095
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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