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Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models

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  • Cai, Zongwu

Abstract

One of the advantages for the varying-coefficient model is to allow the coefficients to vary as smooth functions of other variables and the model can be estimated easily through a simple local quasi-likelihood method. This leads to a simple one-step estimation procedure. We show that such a one-step method cannot be optimal when some coefficient functions possess different degrees of smoothness. This drawback can be attenuated by using a two-step estimation approach. The asymptotic normality and mean-squared errors of the two-step method are obtained and it is also shown that the two-step estimation not only achieves the optimal convergent rate but also shares the same optimality as the ideal case where the other coefficient functions were known. A numerical study is carried out to illustrate the two-step method.

Suggested Citation

  • Cai, Zongwu, 2002. "Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 189-209, July.
  • Handle: RePEc:eee:jmvana:v:82:y:2002:i:1:p:189-209
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    References listed on IDEAS

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    1. Cai, Zongwu & Fan, Jianqing & Yao, Qiwei, 2000. "Functional-coefficient regression models for nonlinear time series," LSE Research Online Documents on Economics 6314, London School of Economics and Political Science, LSE Library.
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    Citations

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    Cited by:

    1. Cai, Zongwu & Li, Qi & Park, Joon Y., 2009. "Functional-coefficient models for nonstationary time series data," Journal of Econometrics, Elsevier, vol. 148(2), pages 101-113, February.
    2. repec:wyi:journl:002108 is not listed on IDEAS
    3. Zongwu Cai & Huaiyu Xiong, 2013. "Effient Estimation of Partially Varying Coefficient Instrumental Variables Models," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    4. Cai, Zongwu & Das, Mitali & Xiong, Huaiyu & Wu, Xizhi, 2006. "Functional coefficient instrumental variables models," Journal of Econometrics, Elsevier, vol. 133(1), pages 207-241, July.
    5. repec:wyi:journl:002112 is not listed on IDEAS
    6. repec:eee:eecrev:v:94:y:2017:i:c:p:126-147 is not listed on IDEAS
    7. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    8. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    9. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    10. Zongwu Cai & Henong Li, 2013. "Convergency and Divergency of Functional Coefficient Weak Instrumental Variables Models," WISE Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. repec:wyi:journl:002114 is not listed on IDEAS
    12. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    13. repec:eee:ecolet:v:156:y:2017:i:c:p:27-31 is not listed on IDEAS
    14. Xialu Liu & Zongwu Cai & Rong Chen, 2015. "Functional coefficient seasonal time series models with an application of Hawaii tourism data," Computational Statistics, Springer, vol. 30(3), pages 719-744, September.
    15. repec:wyi:journl:002096 is not listed on IDEAS

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