High-dimensional instrumental variables regression and confidence sets

By Eric Gautier, Alexandre B. Tsybakov. 2011

158 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/77179cabc7c8fbe081a6efe731fef357f82f8094

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Citations in the corpus

An Overview on the Estimation of Large Covariance and Precision Matrices (2015, unknown): “Here τj serves as an auxiliary variable which ensures that we can use the same regularization parameter λ for estimating different columns of ∆ (Gautier and Tsybakov, 2011). Both the objective function and constraints in (26) contain τj, which ensures that τj is bounded. Zhao and Liu (2014) show tha”
Uniform Inference for High-dimensional Quantile Regression: Linear Functionals and Regression Rank Scores (2017, background): “Results in Gautier and Tsybakov (2011), Juditsky et al. (2012), and Gautier and Tsybakov (2013) can be used to establish valid conservative bounds on the true parameter based on the `∞ norm convergence rate.”
Linear and conic programming estimators in high dimensional errors‐in‐variables models (2014, methodology): “Following [7], we deﬁne them in a more general form, so that the required property is a consequence of the restricted eigenvalue property whenever the latter is satisﬁed.”
A Unified Theory of Confidence Regions and Testing for High-Dimensional Estimating Equations (2015, background): “Inspired by Gautier and Tsybakov (2011), we consider the following estimator β̂: β̂ = argmin ‖β‖1, such that ‖n−1WT (Xβ − Y )‖∞ ≤ λ. Graphical Models via CLIME/SKEPTIC (Cai et al., 2011; Liu et al., 2012b).”
Sparse Models and Methods for Optimal Instruments With an Application to Eminent Domain (2012, background): “Finally, in work that is more recent that the present paper, Gautier and Tsybakov (2011) consider the important case where the structural equation in an instrumental variables model is itself very high-dimensional and propose a new estimation method related to the Dantzig selector and the…”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “For example, if g0 can be approximated by a sparse linear combination of a large set of transformations of X, one can use the methods of Gautier and Tsybakov (2011) to obtain an estimator of g0.”
Improved Matrix Uncertainty Selector (2011, methodology): “Consider now the model with missing data (7) and assume that X is nonrandom.”
High-dimensional econometrics and regularized GMM (2018, background): “The case where p is small and m is large (larger than the sample size n) was originally studied in [7] and the case where both p and m are large is considered in [54], [68], [17], and [70].”
Confidence intervals for causal effects with invalid instruments by using two‐stage hard thresholding with voting (2016, unknown): “This problem is also prevalent in other applications of IVs, most notably in Mendelian randomization (Davey Smith and Ebrahim, 2003, 2004) where the instruments are genetic in nature and some instruments are likely to be invalid because they have pleiotropic effects (Lawlor et al., 2008; Burgess et ”
Instrumental variables estimation with many weak instruments using regularized JIVE (2014, background): “Bai and Ng (2009), BCCH , and Gautier and Tsybakov (2011) provide examples of this approach.”
Challenges of Big Data Analysis (2013, unknown): “DDR1 encodes receptor tyrosine kinases, which plays an important role in the communication of cells with their microenvironment.”