Skip to main content
SpringerLink
Log in

Information Criteria for Statistical Modeling in Data-Rich Era

  • Conference paper
  • First Online:
Econometrics for Financial Applications (ECONVN 2018)

Part of the book series: Studies in Computational Intelligence ((SCI,volume 760))

Included in the following conference series:

  • 2415 Accesses

Abstract

Due to the dramatic development of measuring instruments in recent years, a huge amount of large-scale data has been acquired in all research areas. Along with this, research method has changed, and data-driven methods are becoming important as the fourth scientific methodology. In the data-driven approach, the model is built according to the theory, knowledge, data, and further the purpose of the analysis. Once a model is built, useful information can be extracted from the data through the fitted model. In this data-driven method, it is crucial to use a good model and thud the evaluation of the model is essential in the success of the data-driven approach. This paper outlines the model evaluation criteria such as AIC, GIC, EIC, and so on, focusing on information criteria for evaluating prediction accuracy based on statistical models. Since \(L_1\) regularization is important in recent data analysis, the evaluation of the regularized model is also outlined.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csaki, F. (eds.) 2nd International Symposium in Information Theory, pp. 267–281 (1973). (Reproduced in Breakthroughs in Statistics, vol. I, Foundations and Basic Theory, S. Kots and N.L. Johnson, eds., pp. 610–624. Springer-Verlag, New York, 1992)

    Google Scholar 

  • Akaike, H.: A new look at the statistical model identification. IEEE Trans. Autom. Control AC 19, 716–723 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  • Akaike, H.: Likelihood and the Bayes procedure. In: Bernardo, N.J., DeGroot, M.H., Lindley, D.V., Smith, A.F.M. (eds.) Bayesian Statistics, Valencia, Spain, pp. 141–166. University Press (1980)

    Google Scholar 

  • Akaike, H., Kitagawa, G. (eds.): The Practice of Time Series Analysis. Springer-Verlag, New York (1998)

    MATH  Google Scholar 

  • Ayres, I.: Super Crunchers: Why Thinking-By-Numbers is the New Way To Be Smart. Bantam Books, New York (2007)

    Google Scholar 

  • Bozdogan, H.: Proceeding of the First US/Japan Conference on the Frontiers of Statistical Modeling: An Informational Approach. Kluwer Academic Publishers, Netherlands (1994)

    Google Scholar 

  • Cavanaugh, J.E., Shumway, R.H.: A bootstrap variant of AIC for state-space model selection. Statistica Sinica 7, 469–473 (1997)

    MathSciNet  MATH  Google Scholar 

  • Davison, A.C.: Approximate predictive likelihood. Biometrika 73, 323–332 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Drucker, P.F.: Post-capitalist Society. Routledge, London (1993)

    Google Scholar 

  • Frank, L.E., Friedman, J.H.: A statistical view of some chemometrics regression tools. Technometrics 35(2), 109–135 (1993)

    Article  MATH  Google Scholar 

  • Fu, W.J.: Penalized regressions: the bridge versus the Lasso. J. Comput. Graph. Stat. 7(3), 397–416 (1998)

    MathSciNet  Google Scholar 

  • Good, I.J., Gaskins, R.A.: Nonparametric roughness penalties for probability densities. Biometrika 58, 255–277 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  • Huber, P.J.: The behavior of maximum likelihood estimates under nonstandard conditions. In: Proceedings of the Fifth Berkley Symposium on Statistics, pp. 221–233 (1976)

    Google Scholar 

  • Ishiguro, M., Sakamoto, Y., Kitagawa, G.: Bootstrapping log likelihood and EIC, an extension of AIC. Ann. Inst. Stat. Math. 49(3), 411–434 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  • Kawano, S.: Selection of tuning parameters in bridge regression models via Bayesian information criterion. Stat. Pap. 55(4), 1207–1223 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  • Kitagawa, G., Gersch, W.: A smoothness priors-state space modeling of time series with trend and seasonality. J. Am. Stat. Assoc. 79(386), 378–389 (1984)

    Google Scholar 

  • Kitagawa, G., Gersch, W.: Smoothness Priors Analysis of Time Series. Lecture Notes in Statistics, vol. 116. Springer-Verlag, Heidelberg (1996)

    Google Scholar 

  • Kitagawa, G., Konishi, S.: Bias and variance reduction techniques for bootstrap information criteria. Ann. Inst. Stat. Math. 62(1), 209–234 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  • Konishi, S., Ando, T., Imoto, S.: Bayesian information criteria and smoothing parameter selection in radial basis function networks. Biometrika 91(1), 27–43 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  • Konishi, S., Kitagawa, G.: Generalized information criteria in model selection. Biometrika 83(4), 875–890 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  • Konishi, S., Kitagawa, G.: Information Criteria and Statistical Modeling. Springer Series in Statistics. Springer, New York (2008)

    Book  MATH  Google Scholar 

  • Kullback, S., Leibler, R.A.: On information and sufficiency. Ann. Stat. 22(22), 79–86 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  • Manyika, J., Chui, M., Bughin, J., Brown, B., Dobbs, R., Roxburgh, C., Byers, A.H.: Big Data: The Next Frontier for Innovation, Competition, and Productivity. McKinsey Global Institute, Washington (2011)

    Google Scholar 

  • Matsui, H., Konishi, S.: Variable selection for functional regression models via the L1 regularization. Comput. Stat. Data Anal. 55(12), 3304–3310 (2011)

    Article  MATH  Google Scholar 

  • Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6, 461–464 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  • Shibata, R.: Statistical aspects of model selection. In: Willems, J.C. (ed.) From Data to Model, pp. 215–240. Springer-Verlag, New York (1989)

    Chapter  Google Scholar 

  • Shibata, R.: Bootstrap estimate of Kullback-Leibler information for model selection. Statistica Sinica 7, 375–394 (1997)

    MathSciNet  MATH  Google Scholar 

  • Silverman, B.W.: Some aspects of the spline smoothing approach to nonparametric regression curve fitting (with discussion). J. Roy. Statist. Soc. Ser. B 47, 1–52 (1985). Akaike’s criterion

    MathSciNet  MATH  Google Scholar 

  • Takeuchi, K.: Distributions of information statistics and criteria for adequacy of models. Math. Sci. 153, 12–18 (1976). (in Japanese)

    Google Scholar 

  • Tierney, L., Kadane, J.B.: Accurate approximations for posterior moments and marginal densities. J. Am. Stat. Assoc. 81, 82–86 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  • Umezu, Y., Shimizu, Y., Masuda, H., Ninomiya, Y.: AIC for non-concave penalized likelihood method. arXiv preprint arXiv:1509.01688 (2015)

  • Wahba, G.: Improper priors, spline smoothing and the problem of guarding against model errors in regression. J. Roy. Statist. Soc. Ser. B 40, 364–372 (1978)

    MathSciNet  MATH  Google Scholar 

  • Wahba, G.: Spline Models for Observational Data. Philadelphia (1990)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, 164-8525, Japan

    Genshiro Kitagawa

Authors
  1. Genshiro Kitagawa
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Genshiro Kitagawa .

Editor information

Editors and Affiliations

  1. Banking University HCMC, Ho Chi Minh City, Vietnam

    Ly H. Anh

  2. Banking University HCMC, Ho Chi Minh City, Vietnam

    Le Si Dong

  3. Computer Science Department, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  4. Banking University HCMC, Ho Chi Minh City, Vietnam

    Nguyen Ngoc Thach

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Kitagawa, G. (2018). Information Criteria for Statistical Modeling in Data-Rich Era. In: Anh, L., Dong, L., Kreinovich, V., Thach, N. (eds) Econometrics for Financial Applications. ECONVN 2018. Studies in Computational Intelligence, vol 760. Springer, Cham. https://doi.org/10.1007/978-3-319-73150-6_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-73150-6_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-73149-0

  • Online ISBN: 978-3-319-73150-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation