Skip to main content
SpringerLink
Log in

Identification of Non-Varying Coefficients in Varying-Coefficient Models

  • Original Papers
  • Published:
Acta Mathematicae Applicatae Sinica Aims and scope Submit manuscript

Abstract

A partially varying-coefficient model is one of the useful modelling tools. In this model, some coefficients of a linear model are kept to be constant whilst the others are allowed to vary with another factor. However, rarely can the analysts know a priori which coefficients can be assumed to be constant and which ones are varying with the given factor. Therefore, the identification problem of the constant coefficients should be solved before the partially varying-coefficient model is used to analyze a real-world data set. In this article, a simple test method is proposed to achieve this task, in which the test statistic is constructed as the sample variance of the estimates of each coefficient function in a well-known varying-coefficient model. Moreover two procedures, called F-approximation and three-moment χ 2 approximation, are employed to derive the p-value of the test. Furthermore, some simulations are conducted to examine the performance of the test and the results are satisfactory.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Azzalini, A., Bowman, A. On the use of nonparametric regression for checking linear relationships. J. R. Statist. Soc. B, 55(2):549–557 (1993)

    MATH  MathSciNet  Google Scholar 

  2. Bowman, A.W., Azzalini, A. Applied smoothing techniques for data analysis:the kernel approach with S-plus illustrations. Oxford Science Publication, Oxford, 1997

  3. Buckley, M.J., Eagleson, G.K. An application to the distribution of quadratic forms in normal random variables. Austral. J. Statist., 30 A:150–159 (1988)

    Article  Google Scholar 

  4. Cai, Z., Fan, J., Yao, Q. Functional-coefficient regression models for nonlinear times series. J. Amer. Statist. Assoc., 95(451):941–956 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Cleveland, W.S., Devlin, S.J. Locally weighted regression:an approach to regression analysis by local fitting. J. Amer. Statist. Assoc., 83(403):596–610 (1988)

    Article  Google Scholar 

  6. Eubank, R.L., Spiegelman, C.H. Testing the goodness-of-fit of a linear model via nonparametric regression techniques. J. Amer. Statist. Assoc., 85(410):387–392 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  7. Fan, J., Zhang, C.M., Zhang, J. Generalized likelihood ratio statistic and Wilks phenomenon. Ann. Statist., 29(1):153–193 (2001)

    MATH  MathSciNet  Google Scholar 

  8. Fan, J., Zhang, W. Statistical estimation in varying-coefficient models. Ann. Statist., 27(5):1491–1518 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  9. Fan, J., Zhang, W. Simultaneous confidence bands and hypothesis testing in varying-coefficient models. Scand. J. Statist., 27(4):715–731 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Fotheringham, A.S., Brunsdon, C., Charlton, M. Geographically Weighted Regression–the analysis of spatially varying relationships. Wiley, Chichester, 2002

  11. Härdle, W., Mammen, E. Comparing nonparametric versus parametric regression fits. Ann. Statist., 21(4):1926–1947 (1993)

    MATH  MathSciNet  Google Scholar 

  12. Hart, J.D., Nonparametric smoothing and lack-of-fit tests. Springer-Verlag, New York, 1997

  13. Hastie, T.J., Tibshirani, R.J. Generalized additive models. Chapman and Hall, London, 1990

  14. Hastie, T.J., Tibshirani, R.J. Varying-coefficient models (with discussion). J. R. Statist. Soc. B, 55(4):757–796 (1993)

    MATH  MathSciNet  Google Scholar 

  15. Hoover, D.R., Rice, J.A., Wu, C.O., Yang, L.P. Nonparametric smoothing estimation of time-varying coefficient models with longitudinal data. Biometrika, 85(4):809–822 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Imhof, J.P. Computing the distribution of quadratic forms in normal variables. Biometrika, 48(3 and 4):419–426 (1961)

    MATH  MathSciNet  Google Scholar 

  17. Jayasuriya, B.R. Testing for polynomial regression using nonparametric regression techniques. J. Amer. Statist. Assoc., 91(436):1626–1631 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  18. Mei, C.L., He, S.Y., Wang, Y.H. A note on the nonparametric least-squares test for checking a polynomial relationship. Acta Mathematicae Applicatae Sinica, 19(3):511–520 (2003)

    Article  MATH  Google Scholar 

  19. Zhang, W., Lee, S., Song, X. Local polynomial fitting in semivarying-coefficient model. J. Multivar. Anal., 82(1):166–188 (2002)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Science, Xi’an Jiaotong University, Xi’an 710049, China

    Chang-lin Mei & Chun-xia Zhang

Authors
  1. Chang-lin Mei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Chun-xia Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chang-lin Mei.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mei, Cl., Zhang, Cx. Identification of Non-Varying Coefficients in Varying-Coefficient Models. Acta Mathematicae Applicatae Sinica, English Series 21, 135–144 (2005). https://doi.org/10.1007/s10255-005-0224-0

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-005-0224-0

Keywords

2000 MR Subject Classification

Search

Navigation