IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v82y2002i1p189-209.html
   My bibliography  Save this article

Two-Step Likelihood Estimation Procedure for Varying-Coefficient Models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)92013-5
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. repec:wyi:journl:002112 is not listed on IDEAS
    2. 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.
    3. Goñi, Edwin & Maloney, William F., 2017. "Why don’t poor countries do R&D? Varying rates of factor returns across the development process," European Economic Review, Elsevier, vol. 94(C), pages 126-147.
    4. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Zongwu Cai & Qi Li, 2013. "Some Recent Develop- ments on Nonparametric Econometrics," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    6. 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.
    7. Zongwu Cai & Xiyuan Liu, 2020. "A Functional-Coefficient VAR Model for Dynamic Quantiles with Constructing Financial Network," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202017, University of Kansas, Department of Economics, revised Oct 2020.
    8. Zongwu Cai & Henong Li, 2013. "Convergency and Divergency of Functional Coefficient Weak Instrumental Variables Models," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    9. repec:wyi:journl:002108 is not listed on IDEAS
    10. repec:wyi:journl:002114 is not listed on IDEAS
    11. Zongwu Cai & Huaiyu Xiong, 2013. "Effient Estimation of Partially Varying Coefficient Instrumental Variables Models," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    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. Chen, Xirong & Huang, Ta-Cheng & Li, Qi, 2017. "An alternative bandwidth selection method for estimating functional coefficient models," Economics Letters, Elsevier, vol. 156(C), pages 27-31.
    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. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    16. 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.
    17. Jun Jin & Tiefeng Ma & Jiajia Dai, 2021. "New efficient spline estimation for varying-coefficient models with two-step knot number selection," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 693-712, July.
    18. repec:wyi:journl:002096 is not listed on IDEAS

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Herwartz, H. & Xu, F., 2010. "A functional coefficient model view of the Feldstein-Horioka puzzle," Journal of International Money and Finance, Elsevier, vol. 29(1), pages 37-54, February.
    2. 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.
    3. Cai, Zongwu, 2003. "Nonparametric estimation equations for time series data," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 379-390, May.
    4. Wang, Qihua & Zhang, Riquan, 2009. "Statistical estimation in varying coefficient models with surrogate data and validation sampling," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2389-2405, November.
    5. Kourtellos, Andros & Stengos, Thanasis & Sun, Yiguo, 2022. "Endogeneity In Semiparametric Threshold Regression," Econometric Theory, Cambridge University Press, vol. 38(3), pages 562-595, June.
    6. Heather L. R. Tierney, 2019. "Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(1), pages 39-63, February.
    7. Stolzenburg, Ulrich, 2014. "Growth determinants across time and space: A semiparametric panel data approach," Economics Working Papers 2014-11, Christian-Albrechts-University of Kiel, Department of Economics.
    8. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.
    9. Qiu, Jia & Li, Degao & You, Jinhong, 2015. "SCAD-penalized regression for varying-coefficient models with autoregressive errors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 100-118.
    10. Jose Olmo, 2023. "A nonparametric predictive regression model using partitioning estimators based on Taylor expansions," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(3), pages 294-318, May.
    11. Todorova, Neda & Souček, Michael, 2014. "The impact of trading volume, number of trades and overnight returns on forecasting the daily realized range," Economic Modelling, Elsevier, vol. 36(C), pages 332-340.
    12. Cai, Zongwu & Xu, Xiaoping, 2009. "Nonparametric Quantile Estimations for Dynamic Smooth Coefficient Models," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 371-383.
    13. Tierney, Heather L.R., 2011. "Forecasting and tracking real-time data revisions in inflation persistence," MPRA Paper 34439, University Library of Munich, Germany.
    14. repec:wyi:journl:002108 is not listed on IDEAS
    15. Wang-Li Xu & Li-Xing Zhu, 2008. "Goodness-of-fit testing for varying-coefficient models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 68(2), pages 129-146, September.
    16. Gupta, Rangan & Mwamba, John W. Muteba & Wohar, Mark E., 2018. "The role of partisan conflict in forecasting the U.S. equity premium: A nonparametric approach," Finance Research Letters, Elsevier, vol. 25(C), pages 131-136.
    17. Hossein Hassani & Mohammad Reza Yeganegi & Rangan Gupta, 2019. "Does inequality really matter in forecasting real housing returns of the United Kingdom?," International Economics, CEPII research center, issue 159, pages 18-25.
    18. Zhang, Chun-Xia & Mei, Chang-Lin & Zhang, Jiang-She, 2007. "An empirical study of a test for polynomial relationships in randomly right censored regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6543-6556, August.
    19. Yiqiang Lu & Riquan Zhang, 2009. "Smoothing spline estimation of generalised varying-coefficient mixed model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(7), pages 815-825.
    20. T. Stengos & E. Zacharias, 2006. "Intertemporal pricing and price discrimination: a semiparametric hedonic analysis of the personal computer market," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 371-386, April.
    21. Praveen Kumar Tripathi & Manika Agarwal & Satyanshu K. Upadhyay, 2024. "A Bayes analysis of autoregressive model having functional-coefficients and its application on exchange rate data," METRON, Springer;Sapienza Università di Roma, vol. 82(3), pages 363-391, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:82:y:2002:i:1:p:189-209. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.