Self-normalized Cramér-type large deviations for independent random variables

By Bing-Yi Jing, Qi-Man Shao, Qiying Wang. 2003

194 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research

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Citations in the corpus

Double/De-Biased Machine Learning of Global and Local Parameters Using Regularized Riesz Representers (2018, background): “…weak assumption: the bound λ̄ and the penalty level λ can be chosen proportionally to √ log(p ∨ n)/√n, that is ℓ̃ ≍ √ log(p ∨ n) using self-normalized moderate deviation bounds (Jing et al. (2003); Belloni et al. (2014)) or high-dimensional central limit theorems (Chernozhukov et al. (2017)),…”
Square-Root Lasso: Pivotal Recovery of Sparse Signals via Conic Programming (2010, methodology): “For example, in the Supplementary Material, we provide an alternative condition, based on the use of the self-normalized moderate deviation theory of [9], which results in much weaker growth condition on p in relation to n, but requires much stronger conditions on the moments of regressors.”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, background): “y in 1997 that Gine, Gotze, and Mason [31] found a necessary and sucient condition for the Student statistic to be asymptotically standard normal. Shao [103,104], Nagaev [67], Jing, Shao, and Wang [49], and Wang and Hall [113] studied the probabilities of large deviations. Chistyakov and Gotze [15,1”
Self-normalized limit theorems: A survey (2013, methodology): “Using an example, Chistyakov and Götze (2004a) [12] proved that the result in [37] is sharp.”
Two-Step Lasso Estimation of the Spatial Weights Matrix (2015, unknown): “[30] show with the use of moderate deviation theory in [44] that as T →∞, P (cmax1≤j≤p̄ ‖S1j‖∞ > λ1/T ) = oP(1) where”
Learning L2 Continuous Regression Functionals via Regularized Riesz Representers (2018, background): “When individual heterogeneity in consumer preferences is independent of X and κ is a lower (upper) bound on the derivative of consumption with respect to income across all individuals, then θ0 is an upper (lower) bound on the weighted average over consumers of exact consumer surplus (equivalent vari”
High-dimensional econometrics and regularized GMM (2018, background): “4 on moderate deviations of self-normalized sums extends the results of [80] to show that the moderate deviation inequality holds, up to some corrections, even if the original random variables in the denominator of the self-normalized sum are replaced by suitable estimators.”
Program evaluation and causal inference with high-dimensional data (2013, background): “The proofs in this section rely on the following result due to Jing et al. (2003).”
Testing Many Moment Inequalities (2013, background): “See Theorem 7.4 in Lai, de la Peña, and Shao (2009) or the original paper Jing, Shao, and Wang (2003).”
Double/de-biased machine learning using regularized Riesz representers (2018, methodology): “R.2 is a weak assumption that can be satisﬁed by taking ℓ 1 n = ℓ 2 n = log( p ∨ n ) under weak assumptions on moments, as follows from self-normalized moderate deviation bounds (Jing et al. (2003); Belloni et al. (2014b)), without requiring subgaus-sian tails bounds.”
Pivotal estimation via square-root Lasso in nonparametric regression (2011, methodology): “We rely on moderate deviation theory for selfnormalized sums of [33] to achieve Gaussian-like results in many non-Gaussian cases provided logp = o(n1/3), improving upon results derived in the parametric case that required logp logn, see [12].”
Exponential inequalities for martingales with applications (2013, background): “[22] Jing, B.Y., Shao, Q.M. and Wang, Q., 2003.”
Asymptotic distribution of the largest off-diagonal entry of correlation matrices (2007, methodology): “3 of Jing, Shao and Wang [8] to obtain (3.”