Skip to main content
SpringerLink
Log in

Regularized REML for Estimation in Heteroscedastic Regression Models

  • Conference paper
Nonlinear Mathematics for Uncertainty and its Applications

Part of the book series: Advances in Intelligent and Soft Computing ((AINSC,volume 100))

Abstract

In this paper, we propose a regularized restricted maximum likelihood(REML) method for simultaneous variable selection in heteroscedastic regression models. Under certain regularity conditions, we establish the consistency and asymptotic normality of the resulting estimator. A simulation study is conducted to illustrate the performance of the proposed method.

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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aitkin, M.: Modelling variance heterogeneity in normal regression using GLIM. Appl. Statist. 36, 332–339 (1987)

    Article  Google Scholar 

  2. Engel, J., Huele, A.F.: A generalized linear modeling approach to robust design. Technometrics 38, 365–373 (1996)

    Article  MATH  Google Scholar 

  3. Fan, J.Q., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. Journal of American Statistical Association 96, 1348–1360 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  4. Fan, J.Q., Lv, J.C.: A selective overview of variable selection in high dimensional feature space. Statistica Sinica 20, 101–148 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Harvey, A.C.: Estimating regression models with multiplicative heteroscedasticity. Econometrica 44, 460–465 (1976)

    Article  MathSciNet  Google Scholar 

  6. Harville, D.A.: Bayesian Inference for Variance Components Using Only Error Contrasts. Biometrika 61, 383–385 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lee, Y., Nelder, J.A.: Generalized linear models for the analysis of quality improvement experiments. The Canadian Journal of Statistics 26(1), 95–105 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  8. Nelder, J.A., Lee, Y.: Generalized linear models for the analysis of Taguchi-type experiments. Applied Stochastic Models and Data Analysis 7, 107–120 (1991)

    Article  Google Scholar 

  9. Park, R.E.: Estimation with heteroscedastic error terms. Econometrica 34, 888 (1966)

    Article  Google Scholar 

  10. Smyth, G.K., Verbyla, A.P.: Adjusted likelihood methods for modelling dispersion in generalized linear models. Environmetrics 10, 696–709 (1999)

    Article  Google Scholar 

  11. Taylor, J.T., Verbyla, A.P.: Joint modelling of location and scale parameters of the t distribution. Statistical Modelling 4, 91–112 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  12. Tibshirani, R.: Regression shrinkage and selection via the LASSO. Journal of Royal Statistical Society Series B 58, 267–288 (1996)

    MathSciNet  MATH  Google Scholar 

  13. Verbyla, A.P.: Variance heterogeneity: residual maximum likelihood and diagnostics. Journal of the Royal Statistical Society Series B 52, 493–508 (1993)

    MathSciNet  Google Scholar 

  14. Wang, D.R., Zhang, Z.Z.: Variable selection in joint generalized linear models. Chinese Journal of Applied Probability and Statistics 25, 245–256 (2009)

    MATH  Google Scholar 

  15. Wang, H., Li, R., Tsai, C.: Tuning parameter selectors for the smoothly clipped absolute deviation method. Biometrika 94, 553–568 (2007)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, Chaoyang District, Beijing, 100124, P.R. China

    Dengke Xu & Zhongzhan Zhang

Authors
  1. Dengke Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhongzhan Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. College of Applied Sciences, Beijing University of Technology, 100 Pingleyuan, 100124, Chaoyang District, Beijing, P.R. China

    Shoumei Li , Xia Wang  & Li Guan ,  & 

  2. Department of Systems Design and Informatics, Kyushu Institute of Technology, 680-4, Kawazu, 820-8502, lizuka, Japan

    Yoshiaki Okazaki

  3. Department of Mathematics, Shinshu University, 4-17-1 Wakasato, 380-8553, Nagano, Japan

    Jun Kawabe

  4. Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology, 4259-G3-47, Nagatsuta, Midori-ku, 226-8502, Yokohama, Japan

    Toshiaki Murofushi

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Xu, D., Zhang, Z. (2011). Regularized REML for Estimation in Heteroscedastic Regression Models. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L. (eds) Nonlinear Mathematics for Uncertainty and its Applications. Advances in Intelligent and Soft Computing, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22833-9_60

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22833-9_60

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22832-2

  • Online ISBN: 978-3-642-22833-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation