
Model misspecification and bias for inverse probability weighting and doubly robust estimators
In the causal inference literature a class of semiparametric estimators...
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A debiased distributed estimation for sparse partially linear models in diverging dimensions
We consider a distributed estimation of the doublepenalized least squar...
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HighDimensional Econometrics and Regularized GMM
This chapter presents key concepts and theoretical results for analyzing...
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Semiparametric Inference for Nonmonotone MissingNotatRandom Data: the No SelfCensoring Model
We study the identification and estimation of statistical functionals of...
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Learning a highdimensional classification rule using auxiliary outcomes
Correlated outcomes are common in many practical problems. Based on a de...
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Asymptotic linear expansion of regularized Mestimators
Parametric highdimensional regression analysis requires the usage of re...
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On Stein's Identity and NearOptimal Estimation in Highdimensional Index Models
We consider estimating the parametric components of semiparametric mult...
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High Dimensional MEstimation with Missing Outcomes: A SemiParametric Framework
We consider high dimensional Mestimation in settings where the response Y is possibly missing at random and the covariates X∈R^p can be high dimensional compared to the sample size n. The parameter of interest θ_0 ∈R^d is defined as the minimizer of the risk of a convex loss, under a fully nonparametric model, and θ_0 itself is high dimensional which is a key distinction from existing works. Standard high dimensional regression and series estimation with possibly misspecified models and missing Y are included as special cases, as well as their counterparts in causal inference using 'potential outcomes'. Assuming θ_0 is ssparse (s ≪ n), we propose an L_1regularized debiased and doubly robust (DDR) estimator of θ_0 based on a high dimensional adaptation of the traditional double robust (DR) estimator's construction. Under mild tail assumptions and arbitrarily chosen (working) models for the propensity score (PS) and the outcome regression (OR) estimators, satisfying only some highlevel conditions, we establish finite sample performance bounds for the DDR estimator showing its (optimal) L_2 error rate to be √(s (log d)/ n) when both models are correct, and its consistency and DR properties when only one of them is correct. Further, when both the models are correct, we propose a desparsified version of our DDR estimator that satisfies an asymptotic linear expansion and facilitates inference on low dimensional components of θ_0. Finally, we discuss various of choices of high dimensional parametric/semiparametric working models for the PS and OR estimators. All results are validated via detailed simulations.
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