Uniform Inference for High-Dimensional Linear Models

Confidence intervals and hypothesis testing for high-dimensional regression

Adel Javanmard, Andrea Montanari (2014)

Journal of Machine Learning Research

📍 Section 1.1 (Organization of the Paper), paragraph beginning “It is currently an open question whether successful hypothesis testing can be performed under the weaker assumption $s_0=o(n/\log p)$,” p. 2872 (PDF p. 4).

Confidence intervals for low dimensional parameters in high dimensional linear models

Cun-Hui Zhang, Stephanie Zhang (2014)

Journal of the Royal Statistical Society Series B

On asymptotically optimal confidence regions and tests for high-dimensional models

Sara van de Geer, Peter Bühlmann, Ya'acov Ritov, Ruben Dezeure (2014)

Annals of Statistics

📍 Section 2 (Main results), Theorem 2.1 (asymptotic normality of the desparsified Lasso), p. 1170.