IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2501.15692.html
   My bibliography  Save this paper

Simple Inference on a Simplex-Valued Weight

Author

Listed:
  • Nathan Canen
  • Kyungchul Song

Abstract

In many applications, the parameter of interest involves a simplex-valued weight which is identified as a solution to an optimization problem. Examples include synthetic control methods with group-level weights and various methods of model averaging and forecast combination. The simplex constraint on the weight poses a challenge in statistical inference due to the constraint potentially binding. In this paper, we propose a simple method of constructing a confidence set for the weight and prove that the method is asymptotically uniformly valid. The procedure does not require tuning parameters or simulations to compute critical values. The confidence set accommodates both the cases of point-identification or set-identification of the weight. We illustrate the method with an empirical example.

Suggested Citation

  • Nathan Canen & Kyungchul Song, 2025. "Simple Inference on a Simplex-Valued Weight," Papers 2501.15692, arXiv.org.
  • Handle: RePEc:arx:papers:2501.15692
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2501.15692
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Diaa Al Mohamad & Erik W Van Zwet & Eric Cator & Jelle J Goeman, 2020. "Adaptive critical value for constrained likelihood ratio testing," Biometrika, Biometrika Trust, vol. 107(3), pages 677-688.
    2. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.
    3. Noémi Kreif & Richard Grieve & Dominik Hangartner & Alex James Turner & Silviya Nikolova & Matt Sutton, 2016. "Examination of the Synthetic Control Method for Evaluating Health Policies with Multiple Treated Units," Health Economics, John Wiley & Sons, Ltd., vol. 25(12), pages 1514-1528, December.
    4. G. Elliott & C. Granger & A. Timmermann (ed.), 2006. "Handbook of Economic Forecasting," Handbook of Economic Forecasting, Elsevier, edition 1, volume 1, number 1.
    5. Alberto Abadie & Jérémy L’Hour, 2021. "A Penalized Synthetic Control Estimator for Disaggregated Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1817-1834, October.
    6. Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
    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. Tomasz Serwach, 2023. "The European Union and within‐country income inequalities. The case of the new member states," The World Economy, Wiley Blackwell, vol. 46(7), pages 1890-1939, July.
    2. Tomasz Serwach, 2022. "The European Union and within-country income inequalities. The case of the New Member States," Working Papers hal-03548416, HAL.
    3. Eli Ben‐Michael & Avi Feller & Jesse Rothstein, 2022. "Synthetic controls with staggered adoption," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 351-381, April.
    4. Isaac Loh, 2024. "Inference under partial identification with minimax test statistics," Papers 2401.13057, arXiv.org, revised Apr 2024.
    5. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    6. Roy Cerqueti & Raffaella Coppier & Alessandro Girardi & Marco Ventura, 2022. "The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 46-70.
    7. Zheng Fang & Andres Santos & Azeem M. Shaikh & Alexander Torgovitsky, 2023. "Inference for Large‐Scale Linear Systems With Known Coefficients," Econometrica, Econometric Society, vol. 91(1), pages 299-327, January.
    8. Christoph Breunig & Xiaohong Chen, 2020. "Adaptive, Rate-Optimal Hypothesis Testing in Nonparametric IV Models," Cowles Foundation Discussion Papers 2238R, Cowles Foundation for Research in Economics, Yale University, revised Dec 2021.
    9. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2023. "Constrained Conditional Moment Restriction Models," Econometrica, Econometric Society, vol. 91(2), pages 709-736, March.
    10. Philippe Loyson & Rianne Luijendijk & Sweder van Wijnbergen, 2023. "The pricing of climate transition risk in Europe’s equity market," Working Papers 788, DNB.
    11. Emery, Thomas & Mélon, Lela & Spruk, Rok, 2023. "Does e-procurement matter for economic growth? Subnational evidence from Australia," The Quarterly Review of Economics and Finance, Elsevier, vol. 89(C), pages 318-334.
    12. Chan, Ho Fai & Gangl, Katharina & Supriyadi, Mohammad Wangsit & Torgler, Benno, 2023. "The effects of increased monitoring on high wealth individuals: Evidence from a quasi-natural experiment in Indonesia," Journal of Economic Behavior & Organization, Elsevier, vol. 215(C), pages 244-267.
    13. Christoph Breunig & Xiaohong Chen, 2024. "Adaptive, Rate‐Optimal Hypothesis Testing in Nonparametric IV Models," Econometrica, Econometric Society, vol. 92(6), pages 2027-2067, November.
    14. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    15. Eric Hillebrand & Huiyu Huang & Tae-Hwy Lee & Canlin Li, 2018. "Using the Entire Yield Curve in Forecasting Output and Inflation," Econometrics, MDPI, vol. 6(3), pages 1-27, August.
    16. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    17. Winkelried, Diego, 2012. "Predicting quarterly aggregates with monthly indicators," Working Papers 2012-023, Banco Central de Reserva del Perú.
    18. Daniel Albalate & Germà Bel & Ferran A. Mazaira-Font, 2020. "Ensuring Stability, Accuracy and Meaningfulness in Synthetic Control Methods: The Regularized SHAP-Distance Method," IREA Working Papers 202005, University of Barcelona, Research Institute of Applied Economics, revised Apr 2020.
    19. Faria, Gonçalo & Verona, Fabio, 2023. "Forecast combination in the frequency domain," Bank of Finland Research Discussion Papers 1/2023, Bank of Finland.
    20. Dan Zhu & Qingwei Wang & John Goddard, 2022. "A new hedging hypothesis regarding prediction interval formation in stock price forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 697-717, July.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:2501.15692. 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: http://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.