IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2603.11497.html

Variance Estimation with Dependence and Heterogeneous Means

Author

Listed:
  • Luther Yap

Abstract

This paper develops a framework for variance estimation under dependence and heterogeneous means. This paper shows that consistent estimation of the variance target is impossible in general, and characterizes necessary and sufficient conditions for conservative variance estimation using dual cones. To choose among the valid estimators, this paper formulates three criteria -- minimal correction, pointwise level estimand, and pointwise MSE -- and shows how an eigenvalue truncation solution is optimal under all three criteria. This characterization and solution allow us to assess if existing variance estimators are valid and optimal in their respective settings, and construct the first optimal variance estimator that is simultaneously robust to heterogeneous means and cross-cluster serial correlation.

Suggested Citation

  • Luther Yap, 2026. "Variance Estimation with Dependence and Heterogeneous Means," Papers 2603.11497, arXiv.org, revised Jul 2026.
    • Handle: RePEc:arx:papers:2603.11497
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2603.11497
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    2. Kojevnikov, Denis & Marmer, Vadim & Song, Kyungchul, 2021. "Limit theorems for network dependent random variables," Journal of Econometrics, Elsevier, vol. 222(2), pages 882-908.
    3. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2019. "Empirical Process Results for Exchangeable Arrays," Papers 1906.11293, arXiv.org, revised May 2020.
    4. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    5. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Casini, Alessandro, 2023. "Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstationary models," Journal of Econometrics, Elsevier, vol. 235(2), pages 372-392.
    8. Yap, Luther, 2025. "Asymptotic theory for two-way clustering," Journal of Econometrics, Elsevier, vol. 249(PB).
    9. Ruonan Xu & Luther Yap, 2024. "Clustering with Potential Multidimensionality: Inference and Practice," Papers 2411.13372, arXiv.org.
    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. Chen, Kaicheng & Vogelsang, Timothy J., 2024. "Fixed-b asymptotics for panel models with two-way clustering," Journal of Econometrics, Elsevier, vol. 244(1).
    2. Ulrich Hounyo & Jiahao Lin, 2026. "Bootstrap Inference under General Two-way Clustering with Serially and Spatially Dependent Common Effects," Papers 2605.00709, arXiv.org.
    3. MacKinnon, James G., 2011. "Thirty Years of Heteroskedasticity-Robust Inference," Queen's Economics Department Working Papers 273816, Queen's University - Department of Economics.
    4. Liu, Nan & Liu, Yanbo & Sasaki, Yuya, 2026. "Estimation and inference for causal functions with multi-way clustered data," Journal of Econometrics, Elsevier, vol. 253(C).
    5. Ding, Peng, 2021. "The Frisch–Waugh–Lovell theorem for standard errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    6. Gao, Mengsi & Ding, Peng, 2025. "Causal inference in network experiments: Regression-based analysis and design-based properties," Journal of Econometrics, Elsevier, vol. 252(PA).
    7. Ulrich Hounyo, 2026. "When Does Heteroskedasticity Matter? A Contrast-Specific Theory of Robust Inference," Papers 2607.03331, arXiv.org.
    8. Yap, Luther, 2025. "Asymptotic theory for two-way clustering," Journal of Econometrics, Elsevier, vol. 249(PB).
    9. Casini, Alessandro & Perron, Pierre, 2024. "Prewhitened long-run variance estimation robust to nonstationarity," Journal of Econometrics, Elsevier, vol. 242(1).
    10. Yang, Jingjing & Vogelsang, Timothy J., 2025. "A bias reduced long run variance estimator with a new first-order kernel," Economics Letters, Elsevier, vol. 252(C).
    11. Ulrich Hounyo, 2026. "Adaptive Econometric Inference under Unknown Dependence: Contrast-Local Validity," Papers 2606.22555, arXiv.org, revised Aug 2026.
    12. Kaicheng Chen & Timothy J. Vogelsang, 2023. "Fixed-b Asymptotics for Panel Models with Two-Way Clustering," Papers 2309.08707, arXiv.org, revised Aug 2024.
    13. Peng Ding, 2020. "The Frisch--Waugh--Lovell Theorem for Standard Errors," Papers 2009.06621, arXiv.org.
    14. Harold D Chiang & Bruce E Hansen & Yuya Sasaki, 2022. "Standard errors for two-way clustering with serially correlated time effects," Papers 2201.11304, arXiv.org, revised Dec 2023.
    15. Gustavo Schlemper & Marcelo J. Moreira, 2026. "Confidence Sets under Weak Identification: Theory and Practice," Papers 2604.04279, arXiv.org.
    16. Timothy Conley & Silvia Gonçalves & Christian Hansen, 2018. "Inference with Dependent Data in Accounting and Finance Applications," Journal of Accounting Research, John Wiley & Sons, Ltd., vol. 56(4), pages 1139-1203, September.
    17. Kim, Min Seong & Sun, Yixiao, 2013. "Heteroskedasticity and spatiotemporal dependence robust inference for linear panel models with fixed effects," Journal of Econometrics, Elsevier, vol. 177(1), pages 85-108.
    18. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    19. Thomas Glinnan, 2026. "Design-Based Inference for Time-Series GMM," Papers 2606.31685, arXiv.org.
    20. Cho, Guedae & Kim, MinKyoung & Koo, Won W., 2003. "Relative Agricultural Price Changes In Different Time Horizons," 2003 Annual meeting, July 27-30, Montreal, Canada 22249, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

    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:arx:papers:2603.11497. 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: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    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.