Advanced Search
MyIDEAS: Login

Adaptive varying-coefficient linear models

Contents:

Author Info

  • Jianqing Fan
  • Qiwei Yao
  • Zongwu Cai

Abstract

Varying-coefficient linear models arise from multivariate nonparametric regression, non-linear time series modelling and forecasting, functional data analysis, longitudinal data analysis and others. It has been a common practice to assume that the varying coefficients are functions of a given variable, which is often called an "index". To enlarge the modelling capacity substantially, this paper explores a class of varying-coefficient linear models in which the index is unknown and is estimated as a linear combination of regressors and/or other variables. We search for the index such that the derived varying-coefficient model provides the least squares approximation to the underlying unknown multidimensional regression function. The search is implemented through a newly proposed hybrid backfitting algorithm. The core of the algorithm is the alternating iteration between estimating the index through a one-step scheme and estimating coefficient functions through one-dimensional local linear smoothing. The locally significant variables are selected in terms of a combined use of the "t"-statistic and the Akaike information criterion. We further extend the algorithm for models with two indices. Simulation shows that the methodology proposed has appreciable flexibility to model complex multivariate non-linear structure and is practically feasible with average modern computers. The methods are further illustrated through the Canadian mink-muskrat data in 1925-1994 and the pound-dollar exchange rates in 1974-1983. Copyright 2003 Royal Statistical Society.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/1467-9868.00372
File Function: link to full text
Download Restriction: Access to full text is restricted to subscribers.

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 65 (2003)
Issue (Month): 1 ()
Pages: 57-80

as in new window
Handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:57-80

Contact details of provider:
Postal: 12 Errol Street, London EC1Y 8LX, United Kingdom
Phone: -44-171-638-8998
Fax: -44-171-256-7598
Email:
Web page: http://wileyonlinelibrary.com/journal/rssb
More information through EDIRC

Order Information:
Web: http://ordering.onlinelibrary.wiley.com/subs.asp?ref=1467-9868&doi=10.1111/(ISSN)1467-9868

Related research

Keywords:

References

No references listed on IDEAS
You can help add them by filling out this form.

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Cizek, P. & Haerdle, W. & Spokoiny, V., 2007. "Adaptive Pointwise Estimation in Time-Inhomogeneous Time-Series Models," Discussion Paper 2007-35, Tilburg University, Center for Economic Research.
  2. Huang, Zhensheng & Pang, Zhen & Lin, Bingqing & Shao, Quanxi, 2014. "Model structure selection in single-index-coefficient regression models," Journal of Multivariate Analysis, Elsevier, vol. 125(C), pages 159-175.
  3. Gan, Li & Hsiao, Cheng & Xu, Shu, 2014. "Model specification test with correlated but not cointegrated variables," Journal of Econometrics, Elsevier, vol. 178(P1), pages 80-85.
  4. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
  5. Matthias Fengler & Wolfgang Härdle & Enno Mammen, 2005. "A Dynamic Semiparametric Factor Model for Implied Volatility String Dynamics," SFB 649 Discussion Papers SFB649DP2005-020, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Bruno, Giancarlo, 2008. "Forecasting Using Functional Coefficients Autoregressive Models," MPRA Paper 42335, University Library of Munich, Germany.
  7. Ai, Chunrong & You, Jinhong & Zhou, Yong, 2011. "Statistical inference using a weighted difference-based series approach for partially linear regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 601-618, March.
  8. Liu, Jun M. & Chen, Rong & Yao, Qiwei, 2010. "Nonparametric transfer function models," Journal of Econometrics, Elsevier, vol. 157(1), pages 151-164, July.
  9. Wong, Heung & Ip, Wai-cheung & Zhang, Riquan, 2008. "Varying-coefficient single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1458-1476, January.
  10. Staniswalis, Joan G., 2006. "On fitting generalized non-linear models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 50(7), pages 1818-1839, April.
  11. Harvill, Jane L. & Ray, Bonnie K., 2006. "Functional coefficient autoregressive models for vector time series," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3547-3566, August.
  12. Gloria González-Rivera & Tae-Hwy Lee, 2007. "Nonlinear Time Series in Financial Forecasting," Working Papers 200803, University of California at Riverside, Department of Economics, revised Feb 2008.
  13. Jianqing Fan & Jiancheng Jiang, 2007. "Nonparametric inference with generalized likelihood ratio tests," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(3), pages 409-444, December.
  14. Hwang, Ruey-Ching, 2012. "A varying-coefficient default model," International Journal of Forecasting, Elsevier, vol. 28(3), pages 675-688.
  15. You, Jinhong & Zhou, Xian & Zhou, Yong, 2010. "Statistical inference for panel data semiparametric partially linear regression models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1079-1101, May.
  16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
  17. Sun, Yiguo & Hsiao, Cheng & Li, Qi, 2011. "Measuring correlations of integrated but not cointegrated variables: A semiparametric approach," Journal of Econometrics, Elsevier, vol. 164(2), pages 252-267, October.
  18. Bruno, Giancarlo, 2012. "Consumer confidence and consumption forecast: a non-parametric approach," MPRA Paper 41312, University Library of Munich, Germany.
  19. Battaglia, Francesco, 2005. "Outliers in functional autoregressive time series," Statistics & Probability Letters, Elsevier, vol. 72(4), pages 323-332, May.
  20. Huang, Zhensheng & Zhang, Riquan, 2009. "Efficient estimation of adaptive varying-coefficient partially linear regression model," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 943-952, April.
  21. Jun M. Liu & Rong Chen & Qiwei Yao, 2010. "Nonparametric transfer function models," LSE Research Online Documents on Economics 28868, London School of Economics and Political Science, LSE Library.
  22. Haibo Zhou & Jinhong You & Bin Zhou, 2010. "Statistical inference for fixed-effects partially linear regression models with errors in variables," Statistical Papers, Springer, vol. 51(3), pages 629-650, September.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:bla:jorssb:v:65:y:2003:i:1:p:57-80. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley-Blackwell Digital Licensing) or (Christopher F. Baum).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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