IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v85y2022i1d10.1007_s00184-021-00820-7.html
   My bibliography  Save this article

High-dimensional inference for linear model with correlated errors

Author

Listed:
  • Panxu Yuan

    (University of Science and Technology of China)

  • Xiao Guo

    (University of Science and Technology of China)

Abstract

Temporally correlated error process is commonly encountered in practice and poses significant challenges in high-dimensional statistical analysis. This paper conducts low-dimensional inference for high-dimensional linear models with stationary errors. We adopt the framework of functional dependence measure for adequate accommodation of the error correlation. A new desparsifying Lasso based testing procedure is developed by incorporating a banded estimator of the error autocovariance matrix. Asymptotic normality of the proposed estimator is established by demonstrating the consistency of the banded autocovariance matrix estimator. The result indicates how the range of p is substantially narrower if the moment condition of error weakens or the dependence becomes stronger. We further develop a data-driven choice of the banding parameter. The simulation studies illustrate the satisfactory finite-sample performance of our proposed procedure, and a real data example is also presented for illustration.

Suggested Citation

  • Panxu Yuan & Xiao Guo, 2022. "High-dimensional inference for linear model with correlated errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 21-52, January.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00820-7
    DOI: 10.1007/s00184-021-00820-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-021-00820-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-021-00820-7?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. Chernozhukov, Victor & Härdle, Wolfgang Karl & Huang, Chen & Wang, Weining, 2018. "LASSO-Driven Inference in Time and Space," IRTG 1792 Discussion Papers 2018-021, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    2. Fang Xie & Zhijie Xiao, 2018. "Square†Root LASSO for High†Dimensional Sparse Linear Systems with Weakly Dependent Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(2), pages 212-238, March.
    3. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    4. De Mol, Christine & Giannone, Domenico & Reichlin, Lucrezia, 2008. "Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components?," Journal of Econometrics, Elsevier, vol. 146(2), pages 318-328, October.
    5. Hansheng Wang & Guodong Li & Chih‐Ling Tsai, 2007. "Regression coefficient and autoregressive order shrinkage and selection via the lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(1), pages 63-78, February.
    6. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    7. Liu, Weidong & Wu, Wei Biao, 2010. "Asymptotics Of Spectral Density Estimates," Econometric Theory, Cambridge University Press, vol. 26(4), pages 1218-1245, August.
    8. Cun-Hui Zhang & Stephanie S. Zhang, 2014. "Confidence intervals for low dimensional parameters in high dimensional linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(1), pages 217-242, January.
    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. Xiaorui Zhu & Yichen Qin & Peng Wang, 2023. "Sparsified Simultaneous Confidence Intervals for High-Dimensional Linear Models," Papers 2307.07574, arXiv.org.

    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. Jun Zhu & Hsin‐Cheng Huang & Perla E. Reyes, 2010. "On selection of spatial linear models for lattice data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 389-402, June.
    2. Oguzhan Cepni & I. Ethem Guney & Norman R. Swanson, 2020. "Forecasting and nowcasting emerging market GDP growth rates: The role of latent global economic policy uncertainty and macroeconomic data surprise factors," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(1), pages 18-36, January.
    3. Lenka Zbonakova & Wolfgang Karl Härdle & Weining Wang, 2016. "Time Varying Quantile Lasso," SFB 649 Discussion Papers SFB649DP2016-047, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    4. Toshio Honda, 2021. "The de-biased group Lasso estimation for varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 3-29, February.
    5. Anders Bredahl Kock, 2012. "On the Oracle Property of the Adaptive Lasso in Stationary and Nonstationary Autoregressions," CREATES Research Papers 2012-05, Department of Economics and Business Economics, Aarhus University.
    6. Audrino, Francesco & Camponovo, Lorenzo, 2013. "Oracle Properties and Finite Sample Inference of the Adaptive Lasso for Time Series Regression Models," Economics Working Paper Series 1327, University of St. Gallen, School of Economics and Political Science.
    7. Xinyang Wang & Dehui Wang & Kai Yang, 2021. "Integer-valued time series model order shrinkage and selection via penalized quasi-likelihood approach," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 713-750, July.
    8. Medeiros, Marcelo C. & Mendes, Eduardo F., 2016. "ℓ1-regularization of high-dimensional time-series models with non-Gaussian and heteroskedastic errors," Journal of Econometrics, Elsevier, vol. 191(1), pages 255-271.
    9. Agboola, Oluwagbenga David & Yu, Han, 2023. "Neighborhood-based cross fitting approach to treatment effects with high-dimensional data," Computational Statistics & Data Analysis, Elsevier, vol. 186(C).
    10. Ling Peng & Yan Zhu & Wenxuan Zhong, 2023. "Lasso regression in sparse linear model with $$\varphi $$ φ -mixing errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(1), pages 1-26, January.
    11. Xie, Fang & Xu, Lihu & Yang, Youcai, 2017. "Lasso for sparse linear regression with exponentially β-mixing errors," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 64-70.
    12. Smeekes, Stephan & Wijler, Etienne, 2021. "An automated approach towards sparse single-equation cointegration modelling," Journal of Econometrics, Elsevier, vol. 221(1), pages 247-276.
    13. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
    14. Yoshimasa Uematsu & Takashi Yamagata, 2019. "Estimation of Weak Factor Models," DSSR Discussion Papers 96, Graduate School of Economics and Management, Tohoku University.
    15. Ricardo P. Masini & Marcelo C. Medeiros & Eduardo F. Mendes, 2023. "Machine learning advances for time series forecasting," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 76-111, February.
    16. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    17. Philip Kostov & Thankom Arun & Samuel Annim, 2014. "Financial Services to the Unbanked: the case of the Mzansi intervention in South Africa," Contemporary Economics, University of Economics and Human Sciences in Warsaw., vol. 8(2), June.
    18. Wang, Hansheng & Leng, Chenlei, 2008. "A note on adaptive group lasso," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5277-5286, August.
    19. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    20. Alessandro Gregorio & Francesco Iafrate, 2021. "Regularized bridge-type estimation with multiple penalties," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 921-951, October.

    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:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00820-7. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.