IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v58y2017i1d10.1007_s00362-015-0691-1.html
   My bibliography  Save this article

Principal component selection via adaptive regularization method and generalized information criterion

Author

Listed:
  • Heewon Park

    (Yamaguchi University)

  • Sadanori Konishi

    (Chuo University)

Abstract

The principal component analysis has been widely used in various fields of research (e.g., bioinformatics, medical statistics, etc.), especially high dimensional data analysis. Although crucial components selection is a vital matter in principal components analysis, relatively little attention was paid to this issue. The existing studies for principal component analysis were based on ad-hoc methods (e.g., method with cumulative percent variance or average eigenvalue). We propose a novel method for selecting principal component based on L $$_{1}$$ 1 -type regularized regression modeling. In order to effectively perform for principal component regression, we consider adaptive L $$_{1}$$ 1 -type penalty based on singular values of components, and propose adaptive penalized principal component regression. The proposed method can perform feature selection incorporating explanation power of components for not only high-dimensional predictor variables but also response variable. In sparse regression modeling, choosing the regularization parameter is a crucial issue, since feature selection and estimation heavily depend on the selected regularization parameter. We derive a model selection criterion for choosing the regularization parameter of the proposed adaptive L $$_{1}$$ 1 -type regularization method in line with a generalized information criterion. Monte Carlo simulations and real data analysis demonstrate that the proposed modeling strategies outperform for principal component regression modeling.

Suggested Citation

  • Heewon Park & Sadanori Konishi, 2017. "Principal component selection via adaptive regularization method and generalized information criterion," Statistical Papers, Springer, vol. 58(1), pages 147-160, March.
    • Handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0691-1
    DOI: 10.1007/s00362-015-0691-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-015-0691-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-015-0691-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    2. Dengke Xu & Zhongzhan Zhang & Liucang Wu, 2014. "Variable selection in high-dimensional double generalized linear models," Statistical Papers, Springer, vol. 55(2), pages 327-347, May.
    3. Hansheng Wang & Runze Li & Chih-Ling Tsai, 2007. "Tuning parameter selectors for the smoothly clipped absolute deviation method," Biometrika, Biometrika Trust, vol. 94(3), pages 553-568.
    4. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Erratum to: Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(3), pages 917-918, August.
    5. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    6. Xinfeng Chang & Hu Yang, 2012. "Combining two-parameter and principal component regression estimators," Statistical Papers, Springer, vol. 53(3), pages 549-562, August.
    7. N. Neykov & P. Filzmoser & P. Neytchev, 2014. "Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator," Statistical Papers, Springer, vol. 55(1), pages 187-207, February.
    8. Heewon Park & Fumitake Sakaori, 2013. "Lag weighted lasso for time series model," Computational Statistics, Springer, vol. 28(2), pages 493-504, April.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jianbo Li & Yuan Li & Riquan Zhang, 2017. "B spline variable selection for the single index models," Statistical Papers, Springer, vol. 58(3), pages 691-706, September.
    2. Li Liu & Hao Wang & Yanyan Liu & Jian Huang, 2021. "Model pursuit and variable selection in the additive accelerated failure time model," Statistical Papers, Springer, vol. 62(6), pages 2627-2659, December.
    3. Adriano Zanin Zambom & Gregory J. Matthews, 2021. "Sure independence screening in the presence of missing data," Statistical Papers, Springer, vol. 62(2), pages 817-845, April.
    4. Jun Lu & Lu Lin, 2020. "Model-free conditional screening via conditional distance correlation," Statistical Papers, Springer, vol. 61(1), pages 225-244, February.
    5. Hu Yang & Huilan Liu, 2016. "Penalized weighted composite quantile estimators with missing covariates," Statistical Papers, Springer, vol. 57(1), pages 69-88, March.
    6. Peng, Heng & Lu, Ying, 2012. "Model selection in linear mixed effect models," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 109-129.
    7. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    8. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    9. Gaorong Li & Liugen Xue & Heng Lian, 2012. "SCAD-penalised generalised additive models with non-polynomial dimensionality," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 681-697.
    10. Xia Chen & Liyue Mao, 2020. "Penalized empirical likelihood for partially linear errors-in-variables models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(4), pages 597-623, December.
    11. Tizheng Li & Xiaojuan Kang, 2022. "Variable selection of higher-order partially linear spatial autoregressive model with a diverging number of parameters," Statistical Papers, Springer, vol. 63(1), pages 243-285, February.
    12. Joseph G. Ibrahim & Hongtu Zhu & Ramon I. Garcia & Ruixin Guo, 2011. "Fixed and Random Effects Selection in Mixed Effects Models," Biometrics, The International Biometric Society, vol. 67(2), pages 495-503, June.
    13. Fei Jin & Lung-fei Lee, 2018. "Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices," Econometrics, MDPI, vol. 6(1), pages 1-24, February.
    14. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    15. Zhixuan Fu & Shuangge Ma & Haiqun Lin & Chirag R. Parikh & Bingqing Zhou, 2017. "Penalized Variable Selection for Multi-center Competing Risks Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 379-405, December.
    16. Guang Cheng & Hao Zhang & Zuofeng Shang, 2015. "Sparse and efficient estimation for partial spline models with increasing dimension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 93-127, February.
    17. Zhangong Zhou & Rong Jiang & Weimin Qian, 2013. "LAD variable selection for linear models with randomly censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 287-300, February.
    18. Joel L. Horowitz & Lars Nesheim, 2018. "Using penalized likelihood to select parameters in a random coefficients multinomial logit model," CeMMAP working papers CWP29/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    19. Chen, Kun & Huang, Rui & Chan, Ngai Hang & Yau, Chun Yip, 2019. "Subgroup analysis of zero-inflated Poisson regression model with applications to insurance data," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 8-18.
    20. Sakyajit Bhattacharya & Paul McNicholas, 2014. "A LASSO-penalized BIC for mixture model selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 45-61, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:58:y:2017:i:1:d:10.1007_s00362-015-0691-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.