IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i12p2726-d1172279.html
   My bibliography  Save this article

Research Based on High-Dimensional Fused Lasso Partially Linear Model

Author

Listed:
  • Aifen Feng

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Jingya Fan

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Zhengfen Jin

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Mengmeng Zhao

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

  • Xiaogai Chang

    (School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471023, China)

Abstract

In this paper, a partially linear model based on the fused lasso method is proposed to solve the problem of high correlation between adjacent variables, and then the idea of the two-stage estimation method is used to study the solution of this model. Firstly, the non-parametric part of the partially linear model is estimated using the kernel function method and transforming the semiparametric model into a parametric model. Secondly, the fused lasso regularization term is introduced into the model to construct the least squares parameter estimation based on the fused lasso penalty. Then, due to the non-smooth terms of the model, the subproblems may not have closed-form solutions, so the linearized alternating direction multiplier method (LADMM) is used to solve the model, and the convergence of the algorithm and the asymptotic properties of the model are analyzed. Finally, the applicability of this model was demonstrated through two types of simulation data and practical problems in predicting worker wages.

Suggested Citation

  • Aifen Feng & Jingya Fan & Zhengfen Jin & Mengmeng Zhao & Xiaogai Chang, 2023. "Research Based on High-Dimensional Fused Lasso Partially Linear Model," Mathematics, MDPI, vol. 11(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2726-:d:1172279
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/12/2726/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/12/2726/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Jingyuan & Lou, Lejia & Li, Runze, 2018. "Variable selection for partially linear models via partial correlation," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 418-434.
    2. Yunlu Jiang, 2017. "S-estimator in partially linear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(6), pages 968-977, April.
    3. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    4. Robert Tibshirani & Michael Saunders & Saharon Rosset & Ji Zhu & Keith Knight, 2005. "Sparsity and smoothness via the fused lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 91-108, February.
    5. M. Li & Q. Guo & W. J. Zhai & B. Z. Chen, 2020. "The linearized alternating direction method of multipliers for low-rank and fused LASSO matrix regression model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(13-15), pages 2623-2640, November.
    6. Huang, Jian & Jiao, Yuling & Kang, Lican & Liu, Yanyan, 2021. "Fitting sparse linear models under the sufficient and necessary condition for model identification," Statistics & Probability Letters, Elsevier, vol. 168(C).
    7. Li, Peili & Xiao, Yunhai, 2018. "An efficient algorithm for sparse inverse covariance matrix estimation based on dual formulation," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 292-307.
    Full references (including those not matched with items 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. Wang, Jia & Cai, Xizhen & Li, Runze, 2021. "Variable selection for partially linear models via Bayesian subset modeling with diffusing prior," Journal of Multivariate Analysis, Elsevier, vol. 183(C).
    2. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    3. repec:spo:wpmain:info:hdl:2441/7182 is not listed on IDEAS
    4. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    5. Jinhyun Lee, 2013. "A Consistent Nonparametric Bootstrap Test of Exogeneity," Discussion Paper Series, School of Economics and Finance 201316, School of Economics and Finance, University of St Andrews.
    6. Roberto Martino & Phu Nguyen-Van, 2014. "Labour market regulation and fiscal parameters: A structural model for European regions," Working Papers of BETA 2014-19, Bureau d'Economie Théorique et Appliquée, UDS, Strasbourg.
    7. Mkhadri, Abdallah & Ouhourane, Mohamed, 2013. "An extended variable inclusion and shrinkage algorithm for correlated variables," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 631-644.
    8. De Loecker, Jan & Konings, Jozef, 2003. "Creative Destruction and Productivity Growth in an Emerging Economy: Evidence from Slovenian Manufacturing," IZA Discussion Papers 971, Institute of Labor Economics (IZA).
    9. Bailly, Hugo & Mortier, Frédéric & Giraud, Gaël, 2024. "Empirical analysis of a debt-augmented Goodwin model for the United States," Structural Change and Economic Dynamics, Elsevier, vol. 70(C), pages 619-633.
    10. Eugene Choo & Shannon Seitz & Aloysius Siow, 2008. "The Collective Marriage Matching Model: Identification, Estimation and Testing," Working Papers tecipa-340, University of Toronto, Department of Economics.
    11. Goldstein, Itay & Jiang, Hao & Ng, David T., 2017. "Investor flows and fragility in corporate bond funds," Journal of Financial Economics, Elsevier, vol. 126(3), pages 592-613.
    12. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2023. "Design-Based Identification with Formula Instruments: A Review," NBER Working Papers 31393, National Bureau of Economic Research, Inc.
    13. Chen, Qi & Goldstein, Itay & Jiang, Wei, 2010. "Payoff complementarities and financial fragility: Evidence from mutual fund outflows," Journal of Financial Economics, Elsevier, vol. 97(2), pages 239-262, August.
    14. Vidal-Sanz, Jose M., 1999. "On universal unbiasedness of delta estimators," DES - Working Papers. Statistics and Econometrics. WS 6322, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Polemis, Michael & Tselekounis, Markos, 2019. "Does deregulation drive innovation intensity? Lessons learned from the OECD telecommunications sector," MPRA Paper 92770, University Library of Munich, Germany.
    16. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    17. Flückiger, Matthias & Ludwig, Markus, 2015. "Economic shocks in the fisheries sector and maritime piracy," Journal of Development Economics, Elsevier, vol. 114(C), pages 107-125.
    18. Wongsa-art, Pipat & Kim, Namhyun & Xia, Yingcun & Moscone, Francesco, 2024. "Varying coefficient panel data models and methods under correlated error components: Application to disparities in mental health services in England," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    19. Alena Bicakova & Stepan Jurajda, 2014. "The Quiet Revolution and the Family: Gender Composition of Tertiary Education and Early Fertility Patterns," CERGE-EI Working Papers wp504, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    20. Marco Helbich & Wolfgang Brunauer & Eric Vaz & Peter Nijkamp, 2014. "Spatial Heterogeneity in Hedonic House Price Models: The Case of Austria," Urban Studies, Urban Studies Journal Limited, vol. 51(2), pages 390-411, February.
    21. Temel, Tugrul T., 2001. "A Nonparametric Hypothesis Test Via The Bootstrap Resampling," 2001 Annual meeting, August 5-8, Chicago, IL 20600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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:gam:jmathe:v:11:y:2023:i:12:p:2726-:d:1172279. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.