Confidence Intervals for Low-Dimensional Parameters With High-Dimensional Data

By Cun-Hui Zhang, Shenmin Zhang. 2011

77 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ca93831e7b729bb12fca923bbb8fdde6135a5e71

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

High-Dimensional Statistics with a View Toward Applications in Biology (2014, methodology): “We point out the interesting feature that these estimators β̂corr−Ridge or β̂corr−Lasso are not sparse and they have a Gaussian limiting distribution with known covariance matrix, except for the unknown error variance σ2ε (Bühlmann, 2013; Zhang and Zhang, 2011; van de Geer et al., 2013).”
Confidence sets in sparse regression (2012, unknown): “…for regular fixed linear functionals of θ such as low-dimensional projections, the situation may be different: for instance, in the recent papers of Zhang and Zhang (2011), van de Geer, Bühlmann and Ritov (2013) and Javanmard and Montanari (2013) one-dimensional confidence intervals for a fixed…”
Double/debiased machine learning for treatment and structural parameters (2017, unknown): “Our treatment builds upon the sample-splitting ideas employed in Belloni et al. (2010) and Belloni et al. (2012) who considered sample-splitting in a high-dimensional sparse optimal IV model to weaken the sparsity condition mentioned in the previous paragraph to s n.”
Double machine learning for treatment and causal parameters (2016, methodology): “This second approach represents a generalization of the approach of [31, 52, 57] considered for the case of Lasso-type methods without cross-fitting.”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, methodology): “For a linear model, the procedure is as the one in [52] (or its previous version [51]) and closely related to the method in [23].”
Exact post-selection inference with the lasso (2013, background): “A separate line of work establishes the asymptotic normality of a corrected estimator obtained by “inverting” the KKT conditions (Javanmard and Montanari, 2013; van de Geer et al., 2013; Zhang and Zhang, 2014). imsart-aos ver.”
Uniform post-selection inference for least absolute deviation regression and other Z-estimation problems (2013, result): “The latter feature is critical in achieving uniformity over a large class of data generating processes, similarly to the results for instrumental regression and mean regression studied in [34] and [2, 4, 5].”
Model-assisted inference for treatment effects using regularized calibrated estimation with high-dimensional data (2018, unknown): “On the other hand, if bγ or bα1 is relatively large such that |Sα1 |b(2)γ or |Sγ |b(2)α1 is not op(1), then condition (47) fails, but the right hand side of (45) or (46) can be op(n −1/2) provided bγ = op(1) or bα1 = op(1), bγbα1 = op(n −1/2), and (|Sγ | + |Sα1 |) log(p) = o(n1/2).”
Statistical significance in high-dimensional linear models (2012, methodology): “The diﬃculty in the high-dimensional setting is the construction of the score vector z j from which one can derive a conﬁdence interval for β 0 j : Zhang and Zhang (2011) propose it as the residual vector from the Lasso when regressing X ( j ) against all other variables X ( \ j ) (where X ( J )…”
Double/de-biased machine learning using regularized Riesz representers (2018, result): “Our paper also builds upon and contributes to the literature on the modern orthogonal/debiased estimation and inference [Zhang and Zhang (2014); Belloni et al. (2014a,b, 2015); Javanmard and Montanari (2014a,b, 2015); van de Geer et al. (2014); Ning and Liu (2014); Chernozhukov et al. (2015);…”
Post-Selection Inference for Generalized Linear Models With Many Controls (2013, methodology): “In the context of the linear mean regression model, [9, 10] proposed a “double selection” approach to constructing uniformly valid estimation and inference methods, and [36] used one-step corrections to l1-regularized estimators.”
Regression Analysis for Microbiome Compositional Data (2016, unknown): “These types of debiased estimates were also proposed in Zhang and Zhang (2014) and van de Geer et al. (2014).”
Exact post-selection inference, with application to the lasso (2013, background): “A separate line of work establishes the asymptotic normality of a corrected estimator obtained by “inverting” the KKT conditions (Javanmard and Montanari, 2013; van de Geer et al., 2013; Zhang and Zhang, 2014). imsart-aos ver.”