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Tuning parameter selection in high dimensional penalized likelihood

Journal of the Royal Statistical Society. Series B, Statistical methodology, 2013-06, Vol.75 (3), p.531-552 [Peer Reviewed Journal]

Copyright © 2013 The Royal Statistical Society and Blackwell Publishing Ltd. ;2012 Royal Statistical Society ;Copyright © 2012 The Royal Statistical Society and Blackwell Publishing Ltd ;ISSN: 1369-7412 ;EISSN: 1467-9868 ;DOI: 10.1111/rssb.12001

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Title:
Tuning parameter selection in high dimensional penalized likelihood
Author: Fan, Yingying ; Tang, Cheng Yong
Subjects: Asymptotic methods ; Asymptotic properties ; Complexity ; Criteria ; Data analysis ; Data processing ; Dimensionality ; Gene expression ; Generalization ; Generalized information criterion ; Generalized linear model ; Generalized linear models ; Linear models ; Linear regression ; Mathematical analysis ; Mathematical independent variables ; Mathematical models ; Maximum likelihood estimation ; Maximum likelihood method ; Non Gaussianity ; Optimization ; Oracles ; Parametric models ; Penalized likelihood ; Probability ; Sample size ; Sampling ; Simulation ; Statistical analysis ; Tuning ; Tuning parameter selection ; Variable selection
Is Part Of: Journal of the Royal Statistical Society. Series B, Statistical methodology, 2013-06, Vol.75 (3), p.531-552
Description: Determining how to select the tuning parameter appropriately is essential in penalized likelihood methods for high dimensional data analysis. We examine this problem in the setting of penalized likelihood methods for generalized linear models, where the dimensionality of covariates p is allowed to increase exponentially with the sample size n. We propose to select the tuning parameter by optimizing the generalized information criterion with an appropriate model complexity penalty. To ensure that we consistently identify the true model, a range for the model complexity penalty is identified in the generlized information criterion. We find that this model complexity penalty should diverge at the rate of some power of log(p) depending on the tail probability behaviour of the response variables. This reveals that using the Akaike information criterion or Bayes information criterion to select the tuning parameter may not be adequate for consistently identifying the true model. On the basis of our theoretical study, we propose a uniform choice of the model complexity penalty and show that the approach proposed consistently identifies the true model among candidate models with asymptotic probability 1. We justify the performance of the procedure proposed by numerical simulations and a gene expression data analysis.
Publisher: Oxford: Blackwell Publishing Ltd
Language: English
Identifier: ISSN: 1369-7412
EISSN: 1467-9868
DOI: 10.1111/rssb.12001
Source: Alma/SFX Local Collection

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Tuning parameter selection in high dimensional penalized likelihood

Copyright © 2013 The Royal Statistical Society and Blackwell Publishing Ltd. ;2012 Royal Statistical Society ;Copyright © 2012 The Royal Statistical Society and Blackwell Publishing Ltd ;ISSN: 1369-7412 ;EISSN: 1467-9868 ;DOI: 10.1111/rssb.12001

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