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Andrea Rotnitzky, Ezequiel Smucler, and James Robins’s contribution to the Discussion of ‘Augmented balancing weights as linear regression’ by Bruns-Smith et al.

Rotnitzky、Smucler 与 Robins 对《作为线性回归的增广平衡权重》的讨论

Andrea Rotnitzky, Ezequiel Smucler, James M Robins; Rotnitzky, Smucler and Robins contribution to the Discussion of ‘Augmented balancing weights as linear

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Double/debiased machine learning for treatment and structural parameters

We revisit the classic semi‐parametric problem of inference on a low‐dimensional parameter θ0 in the presence of high‐dimensional nuisance parameters η0. We depart from the classical setting by allowing for η0 to be so high‐dimensional that the traditional assumptions (e.g. Donsker properties) that limit complexity of the parameter space for this object break down. To estimate η0, we consider the use of statistical or machine learning (ML) methods, which are particularly…

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Distribution-Free Prediction Sets

无分布假设的预测集

This paper introduces a new approach to prediction by bringing together two different nonparametric ideas: distribution free inference and nonparametric smoothing. Specifically, we consider the problem of constructing nonparametric tolerance/prediction sets. We start from the general conformal prediction approach and we use a kernel density estimator as a measure of agreement between a sample point and the underlying distribution. The resulting prediction set is shown to be…

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A NEW PROJECTION-TYPE SPLIT-SAMPLE SCORE TEST IN LINEAR INSTRUMENTAL VARIABLES REGRESSION

线性工具变量回归中的新投影型分样本得分检验

In this paper we introduce a new method of projection-type inference and describe it in the context of two stage least squares–based split-sample inference on subsets of structural coefficients in a linear instrumental variables regression model. The use of the new method not only guards against the uncontrolled overrejection of the true value of the parameters of interest but also reduces the conservativeness of the usual method of projection proposed by Dufour and his…

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Adaptive nonparametric confidence sets

自适应非参数置信集

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the diameter of adaptive confidence regions to the minimax rates for testing and…

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Estimation of the Time-Dependent Accelerated Failure Time Model in the Presence of Confounding Factors

存在混淆因素时的时变加速失效时间模型估计

Cox & Oakes (1984, p. 66) introduced the ‘strong version’ of the accelerated failure time model with time-dependent exposures. We provide conditions under which this model could be used to estimate, from observational data, the causal effect of a time-varying exposure or treatment on time to an event of interest in the presence of time-dependent confounding variables. We propose a class of semiparametric tests and estimators for the model parameters. This class contains an…

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Estimation of the time-dependent accelerated failure time model in the presence of confounding factors

存在混杂因素时的时变加速失效时间模型估计

Cox & Oakes (1984, p. 66) introduced the ‘strong version’ of the accelerated failure time model with time-dependent exposures. We provide conditions under which this model could be used to estimate, from observational data, the causal effect of a time-varying exposure or treatment on time to an event of interest in the presence of time-dependent confounding variables. We propose a class of semiparametric tests and estimators for the model parameters. This class contains an…

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Semiparametric estimation of an accelerated failure time model with time-dependent covariates

含时变协变量的加速失效时间模型的半参数估计

A class of semiparametric accelerated failure time models is introduced that are useful for modelling the relationship of survival distributions to time dependent covariates. A class of semiparametric rank estimators is derived for the parameters in this model when the survival data are right censored. These estimates are shown to be consistent, and asymptotically normal with variances that can be consistently estimated. It is also shown that estimators within this class…

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