Unified LASSO Estimation by Least Squares Approximation

By Hansheng Wang, Chenlei Leng. 2007

390 citations recorded by the source corpus.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/4b39cb5f7dbefedb5208d389ca6413cc8b9fca1e

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

ADAPTIVE SEMI-VARYING COEFFICIENT MODEL SELECTION (2012, methodology): “Following Wang and Leng (2007), we define a reference tuning parameter sequence λn according to (2.8) with λ0 = n −3/2h log(n).”
Adaptive penalized quantile regression for high dimensional data (2013, methodology): “However, this would require obtaining a reliable estimate of the inverse of the covariance matrix (see Wang and Leng, 2007), which is a difficult problem in the ultra-high dimensional case.”
Least angle and ℓ1 penalized regression: A review (2008, background): “Wang and Leng (2007) suggest using approximations to loss functions that are quadratic functions of the coefficients, so that solutions can then be computed using the LARS algorithm.”
Multivariate Statistical Analysis (2011, methodology): “A unifying approach which includes the least-squares estimator, shrinkage estimators and various combinations of variable selection and shrinkage has recently been given via a least squares approximation by Wang and Leng (2007).”
Gradient-based kernel method for feature extraction and variable selection (2012, background): “In recent years, extensive studies have been done on variable selection with a sparseness penalty ([6, 16, 18, 23–27, 29, 30] among many others).”
Penalized Quantile Regression for Dynamic Panel Data (2010, positive): “Second, we also consider the least square approximation (LSA) of Wang and Leng (2007).11 They propose BIC2ðplÞ ¼ ðbyl ~yÞ0 bS 1ðbyl ~yÞþðNTÞ 1pllogNT , ð8Þ where byl is the penalized estimate for a given l and ~y is the unpenalized estimate with covariance matrix bS.”
Regularization Parameter Selections via Generalized Information Criterion (2010, background): “Recently, more researchers applied penalized approaches to study variable selections (e.g., Park and Hastie 2007; Wang and Leng 2007; Yuan and Lin 2007; Zhang and Lu 2007; Li and Liang 2008).”
On the distribution of the adaptive LASSO estimator (2008, positive): “Apart from the papers already mentioned, there has been a recent surge of publications establishing the ‘oracle’ property for a variety of penalized maximum likelihood or related estimators (e.g., Bunea (2004), Bunea & McKeague (2005), Fan & Li (2002, 2004), Li & Liang (2007), Wang & Leng (2007) , ”
Shrinkage tuning parameter selection with a diverging number of parameters (2009, methodology): “We follow Wang et al. (2007b) and Wang and Leng (2007), and establish the theorem statement via the following two steps.”
Likelihood-Free Inference by Ratio Estimation (2016, background): “Different schemes to choose λ have been proposed that aim at minimising the prediction risk (Zou et al., 2007; Wang and Leng, 2007; Tibshirani and Taylor, 2012; Dutta et al., 2012).”
Independent screening for single‐index hazard rate models with ultrahigh dimensional features (2011, methodology): “Then we can repeat the arguments of Wang and Leng (2007) and show that, under suitable consistency assumptions for the penalized estimator, there exists a sequence λ n → 0 yielding selection consistency for ˆ βββ λ n and satisfying with S the union of the set of tuning parameters λ which lead to…”
Prediction error of cross-validated Lasso (2015, methodology): “Systematic ways of deterministically choosing the tuning parameter have been proposed by Wang and Leng [40], Zou et al. [44] and Tibshirani and Taylor [36].”
Model Selection via Bayesian Information Criterion for Quantile Regression Models (2014, methodology): “The seminal work of Wang and Leng (2007) followed by Wang, Li, and Tsai (2007b) and Wang, Li, and Leng (2009) suggested to use a BIC-type criterion for choosing the shrinkage parameter in penalized least squares and established the model selection consistency of the resulting procedure.”
Coordinate Descent Methods for the Penalized Semiparametric Additive Hazards Model (2012, methodology): “type, the arguments of Wang and Leng (2007) can be used to show that for p fixed, if n−1f(n)→ 0 and f(n) → ∞, the choice λ̂ := argminλPBIC(λ) entails certain selection consistency properties, depending on the underlying penalization method.”