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C-TMLE for continuous tuning

Abstract : Robust inference of a low-dimensional parameter in a large semi-parametric model relies on external estimators of infinite-dimensional features of the distribution of the data. Typically, only one of the latter is optimized for the sake of constructing a well behaved estimator of the low-dimensional parameter of interest. Optimizing more than one of them for the sake of achieving a better bias-variance trade-off in the estimation of the parameter of interest is the core idea driving the general template of the collaborative targeted minimum loss-based estimation (C-TMLE) procedure. This chapter discusses an implementation/instantiation of the C-TMLE procedure where the optimization is carried out over a set of continuous tuning parameters, like for instance a regularization parameter in a lasso penalty. Under mild assumptions, the resulting TMLE estimator remains asymptotically linear and Gaussian, allowing the construction of confidence regions of given asymptotic levels.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01490380
Contributor : Antoine Chambaz <>
Submitted on : Wednesday, March 15, 2017 - 11:15:37 AM
Last modification on : Tuesday, November 19, 2019 - 10:01:20 AM

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  • HAL Id : hal-01490380, version 1

Citation

Mark van der Laan, Antoine Chambaz, Cheng Ju. C-TMLE for continuous tuning. 2017. ⟨hal-01490380⟩

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