What question did this study set out to answer?

To develop a penalized likelihood framework that selects variables and estimates parameters simultaneously while avoiding the computational expense and stochastic errors of traditional stepwise approaches.

December 1, 2001Journal of the American Statistical Association

Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

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Authors

JFJianqing FanRutgers, The State University of New Jersey RLRunze LiInstitute of Plant Protection

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Implication

Statistical modeling analysis demonstrates simultaneous variable selection and estimation using nonconcave penalties, highlighting oracle efficiency in high-dimensional regression.

Key Points

To develop a penalized likelihood framework that selects variables and estimates parameters simultaneously while avoiding the computational expense and stochastic errors of traditional stepwise approaches.
Designed symmetric, bounded penalty functions that are nonconcave on (0, ∞) and singular at the origin to produce sparse, continuous, and unbiased solutions.
Formulated a new optimization algorithm to solve penalized likelihood equations across generalized linear models, robust regression, and nonparametric smoothing with wavelets and splines.
Derived convergence rates and evaluated finite-sample performance and standard error formula accuracy via extensive simulation studies.
Proved that the proposed estimators achieve oracle properties, matching the performance of a hypothetical model where the true nonzero variables are known in advance.
Demonstrated via simulations that the nonconcave penalized likelihood method compares favorably with conventional variable selection techniques.
Confirmed that the derived standard error formulas yield accurate estimates suitable for practical statistical inference and confidence interval construction.

Cite This Study

Fan et al. (2001) studied this question.

synapsesocial.com/papers/69d88cd8c025a7c015bee01d https://doi.org/10.1198/016214501753382273

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Implication

Statistical modeling analysis demonstrates simultaneous variable selection and estimation using nonconcave penalties, highlighting oracle efficiency in high-dimensional regression.

Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

Discussion

Member takes

Implication

Key Points

Cite This Study

Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties

Discussion

Member takes

Implication

Key Points

Cite This Study

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