Square‐Root LASSO for High‐Dimensional Sparse Linear Systems with Weakly Dependent Errors

Xie, Fang; Zhang, Xiao

doi:10.1111/jtsa.12278

Cited by 7 publications

(4 citation statements)

References 25 publications

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“…Similar invariance properties are also achieved for square-root LASSO estimators (e.g., Belloni, Chernozhukov & Wang, 2011;Xie & Xiao, 2018).…”

Section: Simulation Resultssupporting

confidence: 62%

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The EAS approach for graphical selection consistency in vector autoregression models

Williams¹,

Xie²,

Hannig³

2022

Can J Statistics

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As evidenced by various recent and significant papers within the frequentist literature, along with numerous applications in macroeconomics, genomics, and neuroscience, there continues to be substantial interest in understanding the theoretical estimation properties of high‐dimensional vector autoregression (VAR) models. To date, however, while Bayesian VAR (BVAR) models have been developed and studied empirically (primarily in the econometrics literature), there exist very few theoretical investigations of the repeated‐sampling properties for BVAR models in the literature, and there exist no generalized fiducial investigations of VAR models. In this direction, we construct methodology via the ε‐admissible subsets (EAS) approach for inference based on a generalized fiducial distribution of relative model probabilities over all sets of active/inactive components (graphs) of the VAR transition matrix. We provide a mathematical proof of pairwise and strong graphical selection consistency for the EAS approach for stable VAR(1) models, and demonstrate empirically that it is an effective strategy in high‐dimensional settings.

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“…Similar invariance properties are also achieved for square-root LASSO estimators (e.g., Belloni, Chernozhukov & Wang, 2011;Xie & Xiao, 2018).…”

Section: Simulation Resultssupporting

confidence: 62%

“…In contrast, via our

Λ_{g}

component, the EAS algorithm is scale‐invariant. Similar invariance properties are also achieved for square‐root LASSO estimators (e.g., Belloni, Chernozhukov & Wang, 2011; Xie & Xiao, 2018).…”

Section: Simulation Resultssupporting

confidence: 60%

The EAS approach for graphical selection consistency in vector autoregression models

Williams¹,

Xie²,

Hannig³

2022

Can J Statistics

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show abstract

“…[62] applied Hoeffding's inequality for Markov's chains to deal with this difficulty, see [28] for a review. In time series analysis, [90] studies the square-root Lasso method for HD linear models with α, ρ, φ-mixing or m-dependent errors. The Hoeffding's and Bernstein's CIs for weakly dependent summations can be found in [13].…”

Section: Extensionsmentioning

confidence: 99%

Concentration Inequalities for Statistical Inference

Chen¹

2021

CMR

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This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to sub-exponential, sub-Gamma, and sub-Weibull random variables, and from the mean to the maximum concentration. This review provides results in these settings with some fresh new results. Given the increasing popularity of high-dimensional data and inference, results in the context of high-dimensional linear and Poisson regressions are also provided. We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants.

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“…Miasojedow and Rejchel (2018) applied Hoeffding's inequality for Markov's chains to deal with this difficulty, see Fan et al (2021) for a review. In time series analysis, Xie and Xiao (2018) studies the square-root Lasso method for HD linear models with α, ρ, φ-mixing or m-dependent errors. The Hoeffding's and Bernstein's CIs for weakly dependent summations can be found in Bosq (1998).…”

Section: Contentsmentioning

confidence: 99%

Concentration Inequalities for Statistical Inference

Zhang,

Chen

2020

Preprint

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This paper gives a review of concentration inequalities which are widely employed in non-asymptotical analyses of mathematical statistics in a wide range of settings, from distribution-free to distribution-dependent, from sub-Gaussian to subexponential, sub-Gamma, and sub-Weibull random variables, and from the mean to the maximum concentration. This review provides results in these settings with some fresh new results. Given the increasing popularity of high-dimensional data and inference, results in the context of high-dimensional linear and Poisson regressions are also provided. We aim to illustrate the concentration inequalities with known constants and to improve existing bounds with sharper constants.

show abstract

Square‐Root LASSO for High‐Dimensional Sparse Linear Systems with Weakly Dependent Errors

Cited by 7 publications

References 25 publications

The EAS approach for graphical selection consistency in vector autoregression models

The EAS approach for graphical selection consistency in vector autoregression models

Concentration Inequalities for Statistical Inference

Concentration Inequalities for Statistical Inference

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