IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v32y2017i2d10.1007_s00180-016-0679-x.html
   My bibliography  Save this article

Nonsingular subsampling for regression S estimators with categorical predictors

Author

Listed:
  • Manuel Koller

    (University of Bern
    ETH Zürich)

  • Werner A. Stahel

    (ETH Zürich)

Abstract

Simple random subsampling is an integral part of S estimation algorithms for linear regression. Subsamples are required to be nonsingular. Usually, discarding a singular subsample and drawing a new one leads to a sufficient number of nonsingular subsamples with a reasonable computational effort. However, this procedure can require so many subsamples that it becomes infeasible, especially if levels of categorical variables have low frequency. A subsampling algorithm called nonsingular subsampling is presented, which generates only nonsingular subsamples. When no singular subsamples occur, nonsingular subsampling is as fast as the simple algorithm, and if singular subsamples do occur, it maintains the same computational order. The algorithm works consistently, unless the full design matrix is singular. The method is based on a modified LU decomposition algorithm that combines sample generation with solving the least squares problem. The algorithm may also be useful for ordinary bootstrapping. Since the method allows for S estimation in designs with factors and interactions between factors and continuous regressors, we study properties of the resulting estimators, both in the sense of their dependence on the randomness of the sampling and of their statistical performance.

Suggested Citation

  • Manuel Koller & Werner A. Stahel, 2017. "Nonsingular subsampling for regression S estimators with categorical predictors," Computational Statistics, Springer, vol. 32(2), pages 631-646, June.
    • Handle: RePEc:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0679-x
    DOI: 10.1007/s00180-016-0679-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-016-0679-x
    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/s00180-016-0679-x?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. Koller, Manuel & Stahel, Werner A., 2011. "Sharpening Wald-type inference in robust regression for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2504-2515, August.
    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. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.
    2. Gabriel Okasa & Kenneth A. Younge, 2022. "Sample Fit Reliability," Papers 2209.06631, arXiv.org.
    3. María Morales & Antonio Salmerón & Ana D. Maldonado & Andrés R. Masegosa & Rafael Rumí, 2022. "An Empirical Analysis of the Impact of Continuous Assessment on the Final Exam Mark," Mathematics, MDPI, vol. 10(21), pages 1-21, October.

    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. William Ginn, 2022. "Climate Disasters and the Macroeconomy: Does State-Dependence Matter? Evidence for the US," Economics of Disasters and Climate Change, Springer, vol. 6(1), pages 141-161, March.
    2. Tahereh Dehdarirad & Kalle Karlsson, 2021. "News media attention in Climate Action: latent topics and open access," Scientometrics, Springer;Akadémiai Kiadó, vol. 126(9), pages 8109-8128, September.
    3. Li, J. & Nott, D.J. & Fan, Y. & Sisson, S.A., 2017. "Extending approximate Bayesian computation methods to high dimensions via a Gaussian copula model," Computational Statistics & Data Analysis, Elsevier, vol. 106(C), pages 77-89.
    4. Sean Dougherty & Pietrangelo Biase, 2021. "Who absorbs the shock? An analysis of the fiscal impact of the COVID-19 crisis on different levels of government," International Economics and Economic Policy, Springer, vol. 18(3), pages 517-540, July.
    5. Krantz, Sebastian, 2024. "Patterns of Global and Regional Integration in the East African Community," Kiel Working Papers 2245, Kiel Institute for the World Economy (IfW Kiel), revised 2024.
    6. Rafaty, R. & Dolphin, G. & Pretis, F., 2020. "Carbon pricing and the elasticity of CO2 emissions," Cambridge Working Papers in Economics 20116, Faculty of Economics, University of Cambridge.
    7. Rafaty, Ryan & Dolphin, Geoffroy & Pretis, Felix, 2021. "Carbon Pricing and the Elasticity of CO2 Emissions," RFF Working Paper Series 21-33, Resources for the Future.
    8. Filzmoser, P. & Höppner, S. & Ortner, I. & Serneels, S. & Verdonck, T., 2020. "Cellwise robust M regression," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    9. Amir Abolhassani & Gale Boyd & Majid Jaridi & Bhaskaran Gopalakrishnan & James Harner, 2023. "“Is Energy That Different from Labor?” Similarity in Determinants of Intensity for Auto Assembly Plants," Energies, MDPI, vol. 16(4), pages 1-35, February.
    10. Peter Leoni & Pieter Segaert & Sven Serneels & Tim Verdonck, 2018. "Multivariate constrained robust M‐regression for shaping forward curves in electricity markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(11), pages 1391-1406, November.
    11. T. Kirschstein & Steffen Liebscher, 2019. "Assessing the market values of soccer players – a robust analysis of data from German 1. and 2. Bundesliga," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(7), pages 1336-1349, May.
    12. Kevin Leckey & Dennis Malcherczyk & Melanie Horn & Christine H. Müller, 2023. "Simple powerful robust tests based on sign depth," Statistical Papers, Springer, vol. 64(3), pages 857-882, June.
    13. Stefano Marchetti & Caterina Giusti & Nicola Salvati & Monica Pratesi, 2017. "Small area estimation based on M-quantile models in presence of outliers in auxiliary variables," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 531-555, November.
    14. Krüger, Jens J. & Rhiel, Mathias, 2016. "Determinants of ICT infrastructure: A cross-country statistical analysis," Darmstadt Discussion Papers in Economics 228, Darmstadt University of Technology, Department of Law and Economics.
    15. Morgan, Peter & Regis, Paulo José & Salike, Nimesh, 2015. "Loan-to-Value Policy as a Macroprudential Tool: The Case of Residential Mortgage Loans in Asia," RIEI Working Papers 2015-03, Xi'an Jiaotong-Liverpool University, Research Institute for Economic Integration.
    16. Andreea N. Kiss & Pamela S. Barr, 2015. "New venture strategic adaptation: The interplay of belief structures and industry context," Strategic Management Journal, Wiley Blackwell, vol. 36(8), pages 1245-1263, August.
    17. Eran Mick & Alexandra Tsitsiklis & Natasha Spottiswoode & Saharai Caldera & Paula Hayakawa Serpa & Angela M. Detweiler & Norma Neff & Angela Oliveira Pisco & Lucy M. Li & Hanna Retallack & Kalani Ratn, 2022. "Upper airway gene expression shows a more robust adaptive immune response to SARS-CoV-2 in children," Nature Communications, Nature, vol. 13(1), pages 1-11, December.
    18. Abolhassani, Amir & James Harner, E. & Jaridi, Majid, 2019. "Empirical analysis of productivity enhancement strategies in the North American automotive industry," International Journal of Production Economics, Elsevier, vol. 208(C), pages 140-159.
    19. Yu, Dalei & Ding, Chang & He, Na & Wang, Ruiwu & Zhou, Xiaohua & Shi, Lei, 2019. "Robust estimation and confidence interval in meta-regression models," Computational Statistics & Data Analysis, Elsevier, vol. 129(C), pages 93-118.
    20. Field, Andy Peter Professor & Wilcox, Rand R., 2017. "Robust statistical methods: a primer for clinical psychology and experimental psychopathology researchers," OSF Preprints v3nz4, Center for Open Science.

    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:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0679-x. 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.