Asymptotics for lasso-type estimators

By Keith Knight, Wenjiang J. Fu. 2000

1,520 citations recorded by the source corpus.

Subfields: Numerical Analysis, Statistics and Probability

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Citations in the corpus

Best Subset Selection via a Modern Optimization Lens (2015, background): “…work on Lasso [Bickel, Ritov and Tsybakov (2009), Candès and Plan (2009), Donoho (2006), Efron et al. (2004), Greenshtein and Ritov (2004), Knight and Fu (2000), Meinshausen and Bühlmann (2006), Wainwright (2009), Zhang and Huang (2008), Zhao and Yu (2006)] in terms of algorithms and…”
Joint covariate selection and joint subspace selection for multiple classification problems (2010, background): “Another approach treats the problem as a parameter estimation problem in which the shrinkage induced by a constraint on the l1 norm of the parameter vector yields estimates in which certain components are equal to zero [20, 9, 6].”
High-dimensional graphs and variable selection with the Lasso (2006, methodology): “It is well known that the Lasso, introduced by Tibshirani [16], and known as Basis Pursuit in the context of wavelet regression [2], has a parsimonious property [11].”
On asymptotically optimal confidence regions and tests for high-dimensional models (2013, background): “A major difficulty of the problem is the fact that sparse estimators such as the Lasso do not have a tractable limiting distribution: already in the low-dimensional setting, it depends on the unknown parameter [25] and the convergence to the limit is not uniform.”
Quantile regression for longitudinal data (2004, background): “so δ̂ converges to the the argmin of V0 completing the argument as in Knight and Fu (2000). Part 2. Given the infinite dimensional nature of α there may be some legitimate doubt about the validity of the foregoing approach. A more rigorous argument can be made by explicitly replacing the α̂’s by the”
Statistical Estimation of Correlated Genome Associations to a Quantitative Trait Network (2009, result): “? analogous to the ones previously shown for lasso and fused lasso [32,33].”
Honest confidence regions and optimality in high-dimensional precision matrix estimation (2015, methodology): “We discuss some of the approaches below, but a selected list of papers includes, for instance, Meinshausen and Bühlmann (2006), Friedman et al.”
Variable Selection via A Combination of the L0 and L1 Penalties (2007, methodology): “Theorem 2 is analogous to the asymptotic results for the bridge regression by Knight and Fu (2000). Ifλ0 = 0, then argmin(V) = A−1W andŵn is asymptotically unbiased.”
SparseNet: Coordinate Descent With Nonconvex Penalties (2011, background): “The LASSO enjoys attractive statistical properties (Knight and Fu 2000; Donoho 2006; Meinshausen and Bühlmann 2006; Zhao and Yu 2006).”
On the distribution of the adaptive LASSO estimator (2008, background): “In Knight & Fu (2000), the asymptotic distribution is obtained in a fixed-parameter as well as in a standard local alternatives setup.”
Confidence sets based on penalized maximum likelihood estimators in Gaussian regression (2008, background): “Knight and Fu (2000) study the asymptotic distribution of Bridge estimators and, in particular, of the LASSO estimator.”
The BerHu penalty and the grouped effect (2012, background): “ot degenerated. It is noticeable that there is no integrability condition assumed on the errors . These three assumptions stand for the Huber’s loss. For the penalized least squared estimators (e.g. [14] and [34]) we assume that i are independent identically distributed random variables with mean 0”
Sparsity and smoothness via the fused lasso (2005, methodology): “Asymptotic properties In this section we derive results for the fused lasso that are analogous to those for the lasso (Knight and Fu, 2000).”
On LASSO for predictive regression (2018, positive): “Adopting a standard argument for LASSO as in Knight and Fu (2000) and Zou (2006), we have the following asymptotic distribution for (cid:98) β Slasso .”
A group bridge approach for variable selection (2009, methodology): “When |Aj| = 1, 1 ≤ j ≤ J , this theorem simplifies to the result on lasso of Knight and Fu (2000). 4 Numerical Studies 4.1 Simulation study We use simulation to evaluate the finite sample performance of the group bridge estimator. As a comparison, we also look at the group lasso estimator in the sim”
Computational Statistics and Data Analysis a Note on Adaptive Group Lasso (positive): “Since its first proposal by Tibshirani (1996), the least absolute shrinkage and selection operator (lasso) has generated much interest in the statistical literature (Fu, 1998; Knight and Fu, 2000; Fan and Li, 2001; Efron et al., 2004).”