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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
  • Hardle, Wolfgang

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 established. These theoretical results are derived under the fairly general conditions of absolute regularity (ß-mixing). Application of the test procedure to the West German real GNP data reveals that a partially linear varying coefficient model fits best the data dynamics, a fact that is also confirmed with residual diagnostics.
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Suggested Citation

  • Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    • Handle: RePEc:bes:jnlasa:v:101:y:2006:p:1212-1227
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    1. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
    2. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    3. Yang, Lijian & Tschernig, Rolf, 2002. "Non- And Semiparametric Identification Of Seasonal Nonlinear Autoregression Models," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1408-1448, December.
    4. Jürgen WOLTERS, 1992. "Persistence and Seasonality in output and Employment of the Federal Republic of Germany," Discussion Papers (REL - Recherches Economiques de Louvain) 1992043, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
    5. repec:cup:etheor:v:13:y:1997:i:2:p:214-52 is not listed on IDEAS
    6. Li, Qi, 2000. "Efficient Estimation of Additive Partially Linear Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 41(4), pages 1073-1092, November.
    7. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    8. Fan, J. & Härdle, Wolfgang & Mammen, Enno, 1996. "Direct estimation of low dimensional components in additive models," SFB 373 Discussion Papers 1996,17, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    9. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(2), pages 214-252, April.
    10. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
    11. Sperlich, Stefan & Tjøstheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(2), pages 197-251, April.
    12. Linton, O. B. & Härdle, Wolfgang, 1995. "Estimation of Additive Regression Models with Links," SFB 373 Discussion Papers 1995,48, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Hjellvik, Vidar & Yao, Qiwei & Tjostheim, Dag, 1998. "Linearity testing using local polynominal approximation," LSE Research Online Documents on Economics 6638, London School of Economics and Political Science, LSE Library.
    14. Golubev, Georgi & Härdle, Wolfgang, 2000. "On adaptive estimation in partial linear models," SFB 373 Discussion Papers 2000,21, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. 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.
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    3. 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.
    4. 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.
    5. 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 Science and Technology.
    6. repec:hum:wpaper:sfb649dp2012-045 is not listed on IDEAS
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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).
    14. 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.
    15. 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.
    16. repec:hum:wpaper:sfb649dp2007-023 is not listed on IDEAS
    17. 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.
    18. 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.
    19. Rong Liu & Lijian Yang & Wolfgang K. Härdle, 2013. "Oracally Efficient Two-Step Estimation of Generalized Additive Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 619-631, June.
    20. 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.
    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).
    22. Härdle, Wolfgang Karl & Trück, Stefan, 2010. "The dynamics of hourly electricity prices," SFB 649 Discussion Papers 2010-013, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    23. 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).

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    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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