IDEAS home Printed from https://ideas.repec.org/a/taf/emetrv/v40y2021i1p1-13.html
   My bibliography  Save this article

An upper bound for functions of estimators in high dimensions

Author

Listed:
  • Mehmet Caner
  • Xu Han

Abstract

We provide an upper bound as a random variable for the functions of estimators in high dimensions. This upper bound may help establish the rate of convergence of functions in high dimensions. The upper bound random variable may converge faster, slower, or at the same rate as estimators depending on the behavior of the partial derivative of the function. We illustrate this via three examples. The first two examples use the upper bound for testing in high dimensions, and third example derives the estimated out-of-sample variance of large portfolios. All our results allow for a larger number of parameters, p, than the sample size, n.

Suggested Citation

  • Mehmet Caner & Xu Han, 2021. "An upper bound for functions of estimators in high dimensions," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 1-13, January.
    • Handle: RePEc:taf:emetrv:v:40:y:2021:i:1:p:1-13
    DOI: 10.1080/07474938.2020.1808370
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/07474938.2020.1808370
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/07474938.2020.1808370?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    2. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    3. Caner, Mehmet & Kock, Anders Bredahl, 2018. "Asymptotically honest confidence regions for high dimensional parameters by the desparsified conservative Lasso," Journal of Econometrics, Elsevier, vol. 203(1), pages 143-168.
    4. Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    5. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    6. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    7. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    8. Laurent Callot & Mehmet Caner & A. Özlem Önder & Esra Ulaşan, 2021. "A Nodewise Regression Approach to Estimating Large Portfolios," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(2), pages 520-531, March.
    9. Mehmet Caner & Xu Han & Yoonseok Lee, 2018. "Adaptive Elastic Net GMM Estimation With Many Invalid Moment Conditions: Simultaneous Model and Moment Selection," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 24-46, January.
    10. Mengmeng Ao & Li Yingying & Xinghua Zheng, 2019. "Approaching Mean-Variance Efficiency for Large Portfolios," The Review of Financial Studies, Society for Financial Studies, vol. 32(7), pages 2890-2919.
    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. Caner, Mehmet & Medeiros, Marcelo & Vasconcelos, Gabriel F.R., 2023. "Sharpe Ratio analysis in high dimensions: Residual-based nodewise regression in factor models," Journal of Econometrics, Elsevier, vol. 235(2), pages 393-417.
    2. Mehmet Caner & Qingliang Fan & Yingying Li, 2024. "Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints," Papers 2402.17523, arXiv.org.
    3. Esra Ulasan & A. Özlem Önder, 2023. "Large portfolio optimisation approaches," Journal of Asset Management, Palgrave Macmillan, vol. 24(6), pages 485-497, October.
    4. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.
    5. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    6. Mehmet Caner, 2021. "A Starting Note: A Historical Perspective in Lasso," International Econometric Review (IER), Econometric Research Association, vol. 13(1), pages 1-3, March.
    7. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.
    8. Fan, Qingliang & Wu, Ruike & Yang, Yanrong & Zhong, Wei, 2024. "Time-varying minimum variance portfolio," Journal of Econometrics, Elsevier, vol. 239(2).
    9. Hui, Yongchang & Shi, Mengjie & Wong, Wing-Keung & Zheng, Shurong, 2024. "Pragmatic attitude to large-scale Markowitz’s portfolio optimization and factor-augmented derating," International Review of Financial Analysis, Elsevier, vol. 96(PA).
    10. Tae-Hwy Lee & Ekaterina Seregina, 2024. "Optimal Portfolio Using Factor Graphical Lasso," Journal of Financial Econometrics, Oxford University Press, vol. 22(3), pages 670-695.
    11. Chen, Song Xi & Guo, Bin & Qiu, Yumou, 2023. "Testing and signal identification for two-sample high-dimensional covariances via multi-level thresholding," Journal of Econometrics, Elsevier, vol. 235(2), pages 1337-1354.
    12. Arun G. Chandrasekhar & Victor Chernozhukov & Francesca Molinari & Paul Schrimpf, 2019. "Best Linear Approximations to Set Identified Functions: With an Application to the Gender Wage Gap," NBER Working Papers 25593, National Bureau of Economic Research, Inc.
    13. Li, Kunpeng & Li, Qi & Lu, Lina, 2018. "Quasi maximum likelihood analysis of high dimensional constrained factor models," Journal of Econometrics, Elsevier, vol. 206(2), pages 574-612.
    14. Barigozzi, Matteo & Hallin, Marc & Luciani, Matteo & Zaffaroni, Paolo, 2024. "Inferential theory for generalized dynamic factor models," Journal of Econometrics, Elsevier, vol. 239(2).
    15. Yang Ning & Sida Peng & Jing Tao, 2020. "Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data," Papers 2009.03151, arXiv.org.
    16. Donald, Stephen G. & Hsu, Yu-Chin, 2014. "Estimation and inference for distribution functions and quantile functions in treatment effect models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 383-397.
    17. Hafner, Christian M. & Wang, Linqi, 2024. "Dynamic portfolio selection with sector-specific regularization," Econometrics and Statistics, Elsevier, vol. 32(C), pages 17-33.
    18. Fan, Jianqing & Wang, Weichen & Zhong, Yiqiao, 2019. "Robust covariance estimation for approximate factor models," Journal of Econometrics, Elsevier, vol. 208(1), pages 5-22.
    19. Yu, Xiufan & Yao, Jiawei & Xue, Lingzhou, 2024. "Power enhancement for testing multi-factor asset pricing models via Fisher’s method," Journal of Econometrics, Elsevier, vol. 239(2).
    20. Kan, Raymond & Lassance, Nathan & Wang, Xiaolu, 2023. "The distribution of sample mean-variance portfolio weights," LIDAM Discussion Papers LFIN 2023006, Université catholique de Louvain, Louvain Finance (LFIN).

    More about this item

    Statistics

    Access and download statistics

    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:taf:emetrv:v:40:y:2021:i:1:p:1-13. 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: the person in charge (email available below). General contact details of provider: http://www.tandfonline.com/LECR20 .

    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.