Perturbation bootstrap in adaptive Lasso

Das, Debraj; Gregory, Karl; Lahiri, Soumendra N.

doi:10.1214/18-aos1741

Cited by 18 publications

(17 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark Even though the adaptive elastic net estimators of the nonzero coefficients are asymptotically Normal, some empirical work suggests that convergence is quite slow and that Wald‐type confidence intervals for the coefficients in

β_{0 S_{0}}

will have poor coverage. For example, it was demonstrated in Das et al () that the values of

λ

which ensure good variable selection (larger values of

λ

) tend to result in subnominal coverage of Wald‐type intervals; smaller values of

λ

, under which variable selection performance is poor, result in closer‐to‐nominal coverage of Wald‐type intervals. We emphasize that it is the variable selection result, statement

false(1 false)

of Theorem , which is of primary interest in regularized regression modeling, while the asymptotic Normality result, statement

false(2 false)

of Theorem , comes as a theoretical byproduct, and we do not recommend using it to conduct Wald‐type inference.…”

Section: Technical Resultsmentioning

confidence: 99%

“…Zou () introduced the adaptive lasso and proved an asymptotic Normality result for the estimators of the nonzero regression coefficients to which statement

false(2 false)

of Theorem is analogous; in spite of this result, which would seem to suggest the good performance of Wald‐type intervals, the construction of post‐regularization confidence intervals has remained an area of much on‐going research. For linear regression, Geer et al () and Zhang and Zhang () introduced the desparsified lasso and Das et al () introduced a perturbation bootstrap for the adaptive lasso; investigating adaptations of these methods to group testing could be an area of future research.…”

Section: Technical Resultsmentioning

confidence: 99%

“…Even though the adaptive elastic net estimators of the nonzero coefficients are asymptotically Normal, some empirical work suggests that convergence is quite slow and that Wald-type confidence intervals for the coefficients in 0 0 will have poor coverage. For example, it was demonstrated in Das et al (2017) that the values of which ensure good variable selection (larger values of ) tend to result in subnominal coverage of Wald-type intervals; smaller values of , under which variable selection performance is poor, result in closerto-nominal coverage of Wald-type intervals. We emphasize…”

Section: Theorem 1 Under Assumptions (A1) (A2) and (A3) And Formentioning

confidence: 99%

See 2 more Smart Citations

Adaptive Elastic Net for Group Testing

2018

View full text Add to dashboard Cite

For disease screening, group (pooled) testing can be a cost-saving alternative to oneat-a-time testing, with savings realized through assaying pooled biospecimen (eg, urine, blood, saliva). In many group testing settings, practitioners are faced with the task of conducting disease surveillance. That is, it is often of interest to relate individuals' true disease statuses to covariate information via binary regression. Several authors have developed regression methods for group testing data, which is challenging due to the effects of imperfect testing. That is, all testing outcomes (on pools and individuals) are subject to misclassification, and individuals' true statuses are never observed. To further complicate matters, individuals may be involved in several testing outcomes. For analyzing such data, we provide a novel regression methodology which generalizes and extends the aforementioned regression techniques and which incorporates regularization. Specifically, for model fitting and variable selection, we propose an adaptive elastic net estimator under the logistic regression model which can be used to analyze data from any group testing strategy. We provide an efficient algorithm for computing the estimator along with guidance on tuning parameter selection. Moreover, we establish the asymptotic properties of the proposed estimator and show that it possesses "oracle" properties. We evaluate the performance of the estimator through Monte Carlo studies and illustrate the methodology on a chlamydia data set from the State Hygienic Laboratory in Iowa City.

show abstract

β_{0 S_{0}}

will have poor coverage. For example, it was demonstrated in Das et al () that the values of

λ

which ensure good variable selection (larger values of

λ

) tend to result in subnominal coverage of Wald‐type intervals; smaller values of

λ

, under which variable selection performance is poor, result in closer‐to‐nominal coverage of Wald‐type intervals. We emphasize that it is the variable selection result, statement

false(1 false)

of Theorem , which is of primary interest in regularized regression modeling, while the asymptotic Normality result, statement

false(2 false)

of Theorem , comes as a theoretical byproduct, and we do not recommend using it to conduct Wald‐type inference.…”

Section: Technical Resultsmentioning

confidence: 99%

“…Zou () introduced the adaptive lasso and proved an asymptotic Normality result for the estimators of the nonzero regression coefficients to which statement

false(2 false)

Section: Technical Resultsmentioning

confidence: 99%

Section: Theorem 1 Under Assumptions (A1) (A2) and (A3) And Formentioning

confidence: 99%

See 1 more Smart Citation

Adaptive Elastic Net for Group Testing

2018

View full text Add to dashboard Cite

show abstract

“…The perturbation‐based bootstrap (Das et al . 2019) procedure for penalized regression methods would be interesting to explore in such situations. For distribution‐free predictive inference, split conformal prediction bands (Lei et al .…”

Section: Discussionmentioning

confidence: 99%

Variable selection in nonparametric functional concurrent regression

Ghosal

Maity

2021

Can J Statistics

View full text Add to dashboard Cite

We develop a new method for variable selection in nonparametric functional concurrent regression. The commonly used functional linear concurrent model (FLCM) is far too restrictive in assuming linearity of the covariate effects, which is not necessarily true in many real‐world applications. The nonparametric functional concurrent model (NPFCM), on the other hand, is much more flexible and can capture complex dynamic relationships present between the response and the covariates. We extend the classically used variable selection methods, e.g., group LASSO, group SCAD and group MCP, to perform variable selection in NPFCM. We show via numerical simulations that the proposed variable selection method with the non‐convex penalties can identify the true functional predictors with minimal false‐positive rate and negligible false‐negative rate. The proposed method also provides better out‐of‐sample prediction accuracy compared to the FLCM in the presence of nonlinear effects of the functional predictors. The proposed method's application is demonstrated by identifying the influential predictor variables in two real data studies: a dietary calcium absorption study, and some bike‐sharing data.

show abstract

“…Work on the perturbation bootstrap in the linear regression setup is limited. Some work has been carried out by Chatterjee Das et al (2017). As a variable selection procedure, Tibshirani (1996) introduced the Lasso.…”

Section: Introductionmentioning

confidence: 99%

Distributional consistency of the lasso by perturbation bootstrap

Das

Lahiri

2019

Biometrika

Self Cite

View full text Add to dashboard Cite

Least Absolute Shrinkage and Selection Operator or the Lasso, introduced by Tibshirani (1996), is a popular estimation procedure in multiple linear regression when underlying design has a sparse structure, because of its property that it sets some regression coefficients exactly equal to 0. In this article, we develop a perturbation bootstrap method and establish its validity in approximating the distribution of the Lasso in heteroscedastic linear regression. We allow the underlying covariates to be either random or non-random. We show that the proposed bootstrap method works irrespective of the nature of the covariates, unlike the resample-based bootstrap of Freedman (1981) which must be tailored based on the nature (random vs non-random) of the covariates. Simulation study also justifies our method in finite samples.

show abstract

Perturbation bootstrap in adaptive Lasso

Cited by 18 publications

References 30 publications

Adaptive Elastic Net for Group Testing

Adaptive Elastic Net for Group Testing

Variable selection in nonparametric functional concurrent regression

Distributional consistency of the lasso by perturbation bootstrap

Contact Info

Product

Resources

About