On Parameters of Increasing Dimensions

By Xuming He, Qi-Man Shao. 2000

226 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/fc566da911a1596786abe2874f128f67c0a19391

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Robust Inference on Average Treatment Effects with Possibly More Covariates than Observations (2013, unknown): “We are not aware of any work which covers this case explicitly, though for the first stage, He and Shao (2000) cover linear and logistic regression, and their results easily extend to multinomial logistic models.”
Nonparametric Estimation of an Additive Quantile Regression Model (2004, methodology): “We now apply (3.8) of lemma 3.3 of He and Shao (2000).”
NONCONCAVE PENALIZED M-ESTIMATION WITH A DIVERGING NUMBER OF PARAMETERS (2011, methodology): “To avoid model misspecification and increase the robustness of the estimation, a number of model-free dimension reduction methods have been considered.”
Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors (2012, background): “More generally, this framework also covers the case of multiple linear and nonlinear m-regressions; see, for example, [26] for explicit conditions giving rise to linearizaton (20).”
Group Lasso for high dimensional sparse quantile regression models (2011, background): “…in some cases it can attain the convergence rate arbitrarily close to the oracle rate p p ¯ S /n , the rate which could be achieved when the true sparsity pattern ¯ S were known (see He and Shao, 2000, for convergence rates of general M-estimators in presence of diverging number of parameters).”
VARIABLE SELECTION IN QUANTILE REGRESSION (2009, methodology): “Due to the work of He and Shao (2000) , the solution of the linear quantile regression at (2.4) is still consistent even if the dimension increases with the sample size, but at a speed slower than some root of the sample size.”
Conditional Quantile Estimation for Generalized Autoregressive Conditional Heteroscedasticity Models (2009, background): “Huber (1973) first considered M-estimation of linear regression with continuously differentiable ρ (objective) function, and showed that asymptotic normality can be preserved if m3/n → 0 as n → ∞. Subsequent researchers successfully improved on Huber’s results, including Portnoy (1985), Mammen (1989”
High-dimensional econometrics and regularized GMM (2018, background): “, [75] for explicit conditions giving rise to linearization (1.”
QUANTILE AND PROBABILITY CURVES WITHOUT CROSSING (2007, background): “7See, for example, Chaudhuri (1991) and He and Shao (2000); Belloni and Chernozhukov (2007) have recently extended the results of He and Shao (2000) to the process case and established the functional central limit theorem for an( bQ(u|x) − Q(u|x)) for a fixed x. 14 Thus, if the population curve is…”
Quantile regression in partially linear varying coefficient models (2009, background): “3 of He and Shao [9] that for any L > 0,”
Quantile regression for dynamic panel data with fixed effects (2011, unknown): “He and Shao (2000) and Portnoy (1985).”
Valid Post-Selection Inference in High-Dimensional Approximately Sparse Quantile Regression Models (2013, unknown): “This was proven theoretically in [18] and in [4] under the p→ ∞, p3/n→ 0 regime.”
High‐dimensional quantile regression: Convolution smoothing and concave regularization (2021, methodology): “We refer to Chapter 16 of Koenker et al. (2017) for an overview of the existing results on non-convex regularized QR. Existing work on folded concave penalized QR either impose stringent signal strength assumptions or only establish theoretical guarantees for some local optimum which, due to non-con”
Adaptive penalized quantile regression for high dimensional data (2013, background): “However, both of these estimators achieve the ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n=ðs logðpÞÞ p consistency rate, which is slower than the oracle rate ffiffiffiffiffiffiffi n=s p from He and Shao (2000).”
A modern maximum-likelihood theory for high-dimensional logistic regression (2018, methodology): “Subsequently, [34] quantified the `2 estimation error of the MLE when p log p/n → 0.”
Adaptive Huber Regression (2017, methodology): “-contamination model (Huber 1964), for which a number of depth-based procedures have been developed since the groundbreaking work of Tukey (1975).”