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

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  • Yang, Lijian
  • Härdle, Wolfgang
  • Park, Byeong U.

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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Bibliographic Info

Paper provided by Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes in its series SFB 373 Discussion Papers with number 2002,75.

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Date of creation: 2002
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Handle: RePEc:zbw:sfb373:200275

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Keywords: Equivalent kernels; German real GNP; Local polynomial; Marginal Integration; Rate of convergence;

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  1. J. FAN & Wolfgang HÄRDLE & Enno MAMMEN, 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.
  2. Yang, Lijian & Tschernig, Rolf, 2002. "Non- And Semiparametric Identification Of Seasonal Nonlinear Autoregression Models," Econometric Theory, Cambridge University Press, vol. 18(06), pages 1408-1448, December.
  3. repec:cup:etheor:v:13:y:1997:i:2:p:214-52 is not listed on IDEAS
  4. 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(02), pages 258-289, February.
  5. Oliver Linton & E. Mammen & J. Nielsen, 1999. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 300, London School of Economics and Political Science, LSE Library.
  6. Masry, Elias & Tjøstheim, Dag, 1997. "Additive Nonlinear ARX Time Series and Projection Estimates," Econometric Theory, Cambridge University Press, vol. 13(02), pages 214-252, April.
  7. Hardle, Wolfgang & LIang, Hua & Gao, Jiti, 2000. "Partially linear models," MPRA Paper 39562, University Library of Munich, Germany, revised 01 Sep 2000.
  8. Sperlich, Stefan & Tj stheim, Dag & Yang, Lijian, 2002. "Nonparametric Estimation And Testing Of Interaction In Additive Models," Econometric Theory, Cambridge University Press, vol. 18(02), pages 197-251, April.
  9. Oliver Linton & Enno Mammen & N Nielsen, 2000. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions," STICERD - Econometrics Paper Series /2000/386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. O. B. LINTON & Wolfgang HÄRDLE, 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.
  11. 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).
  12. Franses, Philip Hans, 1996. "Periodicity and Stochastic Trends in Economic Time Series," OUP Catalogue, Oxford University Press, number 9780198774549.
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Cited by:
  1. 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.
  2. Jing Wang & Lijian Yang, 2009. "Efficient and fast spline-backfitted kernel smoothing of additive models," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(3), pages 663-690, September.
  3. 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.
  4. 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.
  5. Olga Klopp & Marianna Pensky, 2013. "Sparse High-dimensional Varying Coefficient Model : Non-asymptotic Minimax Study," Working Papers 2013-30, Centre de Recherche en Economie et Statistique.

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