IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v162y2021ics0167947321001006.html
   My bibliography  Save this article

Fitting jump additive models

Author

Listed:
  • Kang, Yicheng
  • Shi, Yueyong
  • Jiao, Yuling
  • Li, Wendong
  • Xiang, Dongdong

Abstract

Jump regression analysis (JRA) provides a useful tool for estimating discontinuous functional relationships between a response and predictors. Most existing JRA methods consider the problems where there is only one or two predictors. It is unclear whether these methods can be directly extended to cases where there are multiple predictors. A jump additive model and a jump-preserving backfitting procedure are proposed. Jump additive models have the appeal that they make no restrictive parametric assumptions and allow possible discontinuities in the functional relationships, as with univariate JRA methods, but unlike them, jump additive models easily accommodate multiple predictors and the effects of individual predictors on the response can still be visually interpreted, regardless of the number of predictors. The proposed fitting procedure achieves the jump-preserving property by adaptively choosing, in each iteration of the backfitting algorithm, among two one-sided local linear estimates and a two-sided local linear estimate. Theoretical justifications and numerical studies show that it works well in applications. The procedure is also illustrated in analyzing a real data set.

Suggested Citation

  • Kang, Yicheng & Shi, Yueyong & Jiao, Yuling & Li, Wendong & Xiang, Dongdong, 2021. "Fitting jump additive models," Computational Statistics & Data Analysis, Elsevier, vol. 162(C).
    • Handle: RePEc:eee:csdana:v:162:y:2021:i:c:s0167947321001006
    DOI: 10.1016/j.csda.2021.107266
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947321001006
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2021.107266?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Kang, Kee-Hoon & Koo, Ja-Yong & Park, Cheol-Woo, 2000. "Kernel estimation of discontinuous regression functions," Statistics & Probability Letters, Elsevier, vol. 47(3), pages 277-285, April.
    2. 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.
    3. Müller, Hans-Georg & Song, Kai-Sheng, 1997. "Two-stage change-point estimators in smooth regression models," Statistics & Probability Letters, Elsevier, vol. 34(4), pages 323-335, June.
    4. Opsomer, Jean D. & Ruppert, D., 1998. "A Fully Automated Bandwidth Selection Method for Fitting Additive Models," Staff General Research Papers Archive 1176, Iowa State University, Department of Economics.
    5. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    6. Opsomer, Jan & Ruppert, David, 1997. "Fitting a Bivariate Additive Model by Local Polynomial Regression," Staff General Research Papers Archive 1071, Iowa State University, Department of Economics.
    7. Peihua Qiu, 2009. "Jump-preserving surface reconstruction from noisy data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(3), pages 715-751, September.
    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. Ahmed Selema & Mohamed N. Ibrahim & Peter Sergeant, 2022. "Metal Additive Manufacturing for Electrical Machines: Technology Review and Latest Advancements," Energies, MDPI, vol. 15(3), pages 1-18, January.

    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. Yujiao Yang & Qiongxia Song, 2014. "Jump detection in time series nonparametric regression models: a polynomial spline approach," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 325-344, April.
    2. 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.
    3. Irène Gijbels & Alexandre Lambert & Peihua Qiu, 2007. "Jump-Preserving Regression and Smoothing using Local Linear Fitting: A Compromise," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(2), pages 235-272, June.
    4. Opsomer, Jean D., 2000. "Asymptotic Properties of Backfitting Estimators," Journal of Multivariate Analysis, Elsevier, vol. 73(2), pages 166-179, May.
    5. Cui, Yan & Yang, Jun & Zhou, Zhou, 2023. "State-domain change point detection for nonlinear time series regression," Journal of Econometrics, Elsevier, vol. 234(1), pages 3-27.
    6. Chesneau, Christophe & Fadili, Jalal & Maillot, Bertrand, 2015. "Adaptive estimation of an additive regression function from weakly dependent data," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 77-94.
    7. Hegland, Markus & McIntosh, Ian & Turlach, Berwin A., 1999. "A parallel solver for generalised additive models," Computational Statistics & Data Analysis, Elsevier, vol. 31(4), pages 377-396, October.
    8. Youngseon Lee & Seongil Jo & Jaeyong Lee, 2022. "A variational inference for the Lévy adaptive regression with multiple kernels," Computational Statistics, Springer, vol. 37(5), pages 2493-2515, November.
    9. Shujie Ma & Lijian Yang, 2011. "A jump-detecting procedure based on spline estimation," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 67-81.
    10. Koo, Chao, 2018. "Essays on functional coefficient models," Other publications TiSEM ba87b8a5-3c55-40ec-967d-9, Tilburg University, School of Economics and Management.
    11. da Silva, Fernando A. Boeira Sabino, 2002. "Additive nonparametric regression estimation via backfitting and marginal integration: Small sample performance," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 22(2), November.
    12. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    13. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers CWP20/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    14. Peter Malec, 2016. "A Semiparametric Intraday GARCH Model," Cambridge Working Papers in Economics 1633, Faculty of Economics, University of Cambridge.
    15. Kanaya, Shin & Kristensen, Dennis, 2016. "Estimation Of Stochastic Volatility Models By Nonparametric Filtering," Econometric Theory, Cambridge University Press, vol. 32(4), pages 861-916, August.
    16. Li, Xinyi & Wang, Li & Nettleton, Dan, 2019. "Sparse model identification and learning for ultra-high-dimensional additive partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 204-228.
    17. Isabel Casas & Irene Gijbels, 2009. "Unstable volatility functions: the break preserving local linear estimator," CREATES Research Papers 2009-48, Department of Economics and Business Economics, Aarhus University.
    18. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    19. Yicheng Kang & Xiaodong Gong & Jiti Gao & Peihua Qiu, 2016. "Error-in-Variables Jump Regression Using Local Clustering," Monash Econometrics and Business Statistics Working Papers 13/16, Monash University, Department of Econometrics and Business Statistics.
    20. Hongyu An & Boping Tian, 2024. "Varying Index Coefficient Model for Tail Index Regression," Mathematics, MDPI, vol. 12(13), pages 1-35, June.

    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:csdana:v:162:y:2021:i:c:s0167947321001006. 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/locate/csda .

    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.