Scaled sparse linear regression

Sun, Tingni; Zhang, Cun Hui

doi:10.1093/biomet/ass043

Cited by 428 publications

(490 citation statements)

References 26 publications

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“…In general, the asymptotic equivalence (4.7) follows from the orthogonality of parameters β and σ 2 in the log-likelihood function, rather than the use of the Lasso estimators β and σ 2 . This implies that, for the estimation of (β, σ), we can use alternative estimators such as the scaled Lasso (Sun and Zhang, 2012),…”

Section: Estimation Of Unknown Variance σmentioning

confidence: 99%

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

Ning

Liu²

2017

Ann. Statist.

256

327

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We consider the problem of uncertainty assessment for low dimensional components in high dimensional models. Specifically, we propose a decorrelated score function to handle the impact of high dimensional nuisance parameters. We consider both hypothesis tests and confidence regions for generic penalized M-estimators. Unlike most existing inferential methods which are tailored for individual models, our approach provides a general framework for high dimensional inference and is applicable to a wide range of applications. From the testing perspective, we develop general theorems to characterize the limiting distributions of the decorrelated score test statistic under both null hypothesis and local alternatives. These results provide asymptotic guarantees on the type I errors and local powers of the proposed test. Furthermore, we show that the decorrelated score function can be used to construct point estimators that are semiparametrically efficient and the optimal confidence regions. We also generalize this framework to broaden its applications. First, we extend it to handle high dimensional null hypothesis, where the number of parameters of interest can increase exponentially fast with the sample size. Second, we establish the theory for model misspecification. Third, we go beyond the likelihood framework, by introducing the generalized score test based on general loss functions. Thorough numerical studies are conducted to back up the developed theoretical results.

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Section: Estimation Of Unknown Variance σmentioning

confidence: 99%

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

Ning

Liu²

2017

Ann. Statist.

256

327

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“…Scaled sparse linear regression by Sun and Zhang (2012) gives a general approach to regression and penalization, with special focus on the LASSO. The idea is to estimate the parameters in the model and the noise level.…”

Section: Related Workmentioning

confidence: 99%

“…Oracle inequalities are proved for prediction, estimation of noise level and regression coefficients. An implementation can be found in the R package scalreg (Sun 2013), the method can be used with the function scalreg.…”

Section: Related Workmentioning

confidence: 99%

SpaSM: A MATLAB Toolbox for Sparse Statistical Modeling

Sjöstrand¹,

Clemmensen²,

Larsen³

et al. 2018

J. Stat. Soft.

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Applications in biotechnology such as gene expression analysis and image processing have led to a tremendous development of statistical methods with emphasis on reliable solutions to severely underdetermined systems. Furthermore, interpretations of such solutions are of importance, meaning that the surplus of inputs has been reduced to a concise model. At the core of this development are methods which augment the standard linear models for regression, classification and decomposition such that sparse solutions are obtained. This toolbox aims at making public available carefully implemented and well-tested variants of the most popular of such methods for the MATLAB programming environment. These methods consist of easy-to-read yet efficient implementations of various coefficient-path following algorithms and implementations of sparse principal component analysis and sparse discriminant analysis which are not available in MATLAB. The toolbox builds on code made public in 2005 and which has since been used in several studies.

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“…To integrate information from multiple GWAS, we propose the following optimization problem Where γ is the regularization parameter controlling the sparsity of closely related to the scaled Lasso problem [21]. Here we emphasize on integration of information from multiple GWAS and use the group penalty to achieve this goal.…”

Section: Algorithmmentioning

confidence: 99%

A Penalized Regression Approach for Integrative Analysis in Gen ome- Wide Association Studies

F¹

2015

J Biom Biostat

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Over one thousand genome-wide association studies (GWAS) have been conducted in the past decade. Increasing biological evidence suggests the polygenic genetic architecture of complex traits: a complex trait is affected by many risk variants with small or moderate effects jointly. Meanwhile, recent progress in GWAS suggests that complex human traits may share common genetic bases, which is known as "pleiotropy". To further improve statistical power of detecting risk genetic variants in GWAS, we propose a penalized regression method to analyze the GWAS dataset of primary interest by incorporating information from other related GWAS. The proposed method does not require the individual-level of genotype and phenotype data from other related GWAS, making it useful when only summary statistics are available.method. Simulation studies showed that the proposed approach had satisfactory performance. We applied the proposed method to analyze a body mass index (BMI) GWAS dataset from a European American (EA) population and achieved improvement over single GWAS analysis.

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Scaled sparse linear regression

Cited by 428 publications

References 26 publications

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

A general theory of hypothesis tests and confidence regions for sparse high dimensional models

SpaSM: A MATLAB Toolbox for Sparse Statistical Modeling

A Penalized Regression Approach for Integrative Analysis in Gen ome- Wide Association Studies

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