Iterative conditional maximization algorithm for nonconcave penalized likelihood

Yiyun Zhang, Runze Li

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Variable selection via penalized likelihood has received considerable attention recently. Penalized likelihood estimators with properly chosen penalty functions possess nice properties. In practice, optimizing the penalized likelihood function is often challenging because the object function may be nondiffer-entiable and/or nonconcave. Existing algorithms such as the local quadratic approximation (LQA) algorithm share a similar drawback of backward selection that once a variable is deleted, it is essentially left out of the final model. We propose the iterative conditional maximization (ICM) algorithm to address the aforementioned drawback. It utilizes the characteristics of the nonconcave penalized likelihood and enjoys fast convergence. Three simulation studies, in linear, logistic, and Poisson regression, together with one real data analysis, are conducted to assess the performance of the ICM algorithm.

Original languageEnglish (US)
Title of host publicationNonparametric Statistics and Mixture Models
Subtitle of host publicationA Festschrift in Honor of Thomas P Hettmansperger
PublisherWorld Scientific Publishing Co.
Pages336-351
Number of pages16
ISBN (Electronic)9789814340564
ISBN (Print)9814340553, 9789814340557
DOIs
StatePublished - Jan 1 2011

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Penalized Likelihood
Poisson Regression
Quadratic Approximation
Local Approximation
Penalty Function
Variable Selection
Logistic Regression
Likelihood Function
Linear regression
Approximation Algorithms
Data analysis
Simulation Study
Estimator

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Zhang, Y., & Li, R. (2011). Iterative conditional maximization algorithm for nonconcave penalized likelihood. In Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger (pp. 336-351). World Scientific Publishing Co.. https://doi.org/10.1142/9789814340564_0020
Zhang, Yiyun ; Li, Runze. / Iterative conditional maximization algorithm for nonconcave penalized likelihood. Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., 2011. pp. 336-351
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Zhang, Y & Li, R 2011, Iterative conditional maximization algorithm for nonconcave penalized likelihood. in Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., pp. 336-351. https://doi.org/10.1142/9789814340564_0020

Iterative conditional maximization algorithm for nonconcave penalized likelihood. / Zhang, Yiyun; Li, Runze.

Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co., 2011. p. 336-351.

Research output: Chapter in Book/Report/Conference proceedingChapter

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Zhang Y, Li R. Iterative conditional maximization algorithm for nonconcave penalized likelihood. In Nonparametric Statistics and Mixture Models: A Festschrift in Honor of Thomas P Hettmansperger. World Scientific Publishing Co. 2011. p. 336-351 https://doi.org/10.1142/9789814340564_0020