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Estimation and testing for varying coefficients in additive models with marginal integration

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  • Yang, Lijian
  • Park, Byeong U.
  • Xue, Lan
  • Härdle, Wolfgang Karl

Abstract

We propose marginal integration estimation and testing methods for the coefficients of varying coefficient multivariate regression model. Asymptotic distribution theory is developed for the estimation method which enjoys the same rate of convergence as univariate function estimation. For the test statistic, asymptotic normal theory is es- tablished. These theoretical results are derived under the fairly general conditions of absolute regularity (b-mixing). Application of the test procedure to the West Ger- man real GNP data reveals that a partially linear varying coefficient model is best parsimonious in fitting the data dynamics, a fact that is also confirmed with residual diagnostics.

Suggested Citation

  • Yang, Lijian & Park, Byeong U. & Xue, Lan & Härdle, Wolfgang Karl, 2005. "Estimation and testing for varying coefficients in additive models with marginal integration," SFB 649 Discussion Papers 2005-047, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    • Handle: RePEc:zbw:sfb649:sfb649dp2005-047
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    Cited by:

    1. Lee, Kyeongeun & Lee, Young K. & Park, Byeong U. & Yang, Seong J., 2018. "Time-dynamic varying coefficient models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 123(C), pages 50-65.
    2. Song, Qiongxia & Yang, Lijian, 2010. "Oracally efficient spline smoothing of nonlinear additive autoregression models with simultaneous confidence band," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2008-2025, October.
    3. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    4. Ying Wang & Peter C. B. Phillips & Yundong Tu, 2024. "Limit Theory and Inference in Non-cointegrated Functional Coefficient Regression," Cowles Foundation Discussion Papers 2399, Cowles Foundation for Research in Economics, Yale University.
    5. repec:hum:wpaper:sfb649dp2007-023 is not listed on IDEAS
    6. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Center for Research in Economics and Statistics.
    7. Miao Yang & Lan Xue & Lijian Yang, 2016. "Variable selection for additive model via cumulative ratios of empirical strengths total," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(3), pages 595-616, September.
    8. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 663-690, September.
    9. Yang, Seong J. & Park, Byeong U., 2014. "Efficient estimation for partially linear varying coefficient models when coefficient functions have different smoothing variables," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 100-113.
    10. 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.
    11. 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.
    12. Lv, Shaogao & Fan, Zengyan & Lian, Heng & Suzuki, Taiji & Fukumizu, Kenji, 2020. "A reproducing kernel Hilbert space approach to high dimensional partially varying coefficient model," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    13. Rui Li & Yuanyuan Zhang, 2021. "Two-stage estimation and simultaneous confidence band in partially nonlinear additive model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(8), pages 1109-1140, November.
    14. Tu, Yundong & Wang, Ying, 2022. "Spurious functional-coefficient regression models and robust inference with marginal integration," Journal of Econometrics, Elsevier, vol. 229(2), pages 396-421.
    15. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    16. Stefan Sperlich & Raoul Theler, 2015. "Modeling heterogeneity: a praise for varying-coefficient models in causal analysis," Computational Statistics, Springer, vol. 30(3), pages 693-718, September.
    17. Mammen, Enno & Park, Byeong U. & Schienle, Melanie, 2012. "Additive models: Extensions and related models," SFB 649 Discussion Papers 2012-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    18. Stefan Trück & Wolfgang Härdle & Rafal Weron, 2012. "The relationship between spot and futures CO2 emission allowance prices in the EU-ETS," HSC Research Reports HSC/12/02, Hugo Steinhaus Center, Wroclaw University of Technology.
    19. 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.
    20. Han, Kyunghee & Lee, Young K. & Park, Byeong U., 2020. "Smooth backfitting for errors-in-variables varying coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    21. Wang, Taining & Henderson, Daniel J., 2022. "Estimation of a varying coefficient, fixed-effects Cobb–Douglas production function in levels," Economics Letters, Elsevier, vol. 213(C).

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    More about this item

    Keywords

    Equivalent kernels; German real GNP; Local polynomial; Marginal integration; Rate of convergence;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General

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