IDEAS home Printed from https://ideas.repec.org/a/vrs/offsta/v39y2023i4p459-487n2.html

Block Weighted Least Squares Estimation for Nonlinear Cost-based Split Questionnaire Design

Author

Listed:
  • Li Yang

    (Renmin University of China, Center for Applied Statistics and School of Statistics, att: Cunjie Lin, 59 Zhongguancun St, Beijing 100872, China.)

  • Qi Le

    (Renmin University of China, Center for Applied Statistics and School of Statistics, att: Cunjie Lin, 59 Zhongguancun St, Beijing 100872, China.)

  • Qin Yichen

    (University of Cincinnati, Department of Operations, Business Analytics, and Information Systems Cincinnati, Ohio, U.S.A.)

  • Lin Cunjie

    (Renmin University of China, Center for Applied Statistics and School of Statistics, att: Cunjie Lin, 59 Zhongguancun St, Beijing 100872, China.)

  • Yang Yuhong

    (University of Minnesota, School of Statistics Minneapolis, U.S.A.)

Abstract

In this study, we advocate a two-stage framework to deal with the issues encountered in surveys with long questionnaires. In Stage I, we propose a split questionnaire design (SQD) developed by minimizing a quadratic cost function while achieving reliability constraints on estimates of means, which effectively reduces the survey cost, alleviates the burden on the respondents, and potentially improves data quality. In Stage II, we develop a block weighted least squares (BWLS) estimator of linear regression coefficients that can be used with data obtained from the SQD obtained in Stage I. Numerical studies comparing existing methods strongly favor the proposed estimator in terms of prediction and estimation accuracy. Using the European Social Survey (ESS) data, we demonstrate that the proposed SQD can substantially reduce the survey cost and the number of questions answered by each respondent, and the proposed estimator is much more interpretable and efficient than present alternatives for the SQD data.

Suggested Citation

  • Li Yang & Qi Le & Qin Yichen & Lin Cunjie & Yang Yuhong, 2023. "Block Weighted Least Squares Estimation for Nonlinear Cost-based Split Questionnaire Design," Journal of Official Statistics, Sciendo, vol. 39(4), pages 459-487, December.
    • Handle: RePEc:vrs:offsta:v:39:y:2023:i:4:p:459-487:n:2
    DOI: 10.2478/jos-2023-0022
    as

    Download full text from publisher

    File URL: https://doi.org/10.2478/jos-2023-0022
    Download Restriction: no
    File URL: https://libkey.io/10.2478/jos-2023-0022?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
    ---><---

    References listed on IDEAS

    as
    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Christian Schnaudt & Michael Weinhardt & Rory Fitzgerald & Stefan Liebig, 2014. "The European Social Survey: Contents, Design, and Research Potential," Schmollers Jahrbuch : Journal of Applied Social Science Studies / Zeitschrift für Wirtschafts- und Sozialwissenschaften, Duncker & Humblot, Berlin, vol. 134(4), pages 487-506.
    3. James O. Chipperfield & Margo L. Barr & David. G. Steel, 2018. "Split Questionnaire Designs: collecting only the data that you need through MCAR and MAR designs," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(8), pages 1465-1475, June.
    4. Chipperfield, James O. & Steel, David G., 2012. "Multivariate random effect models with complete and incomplete data," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 146-155.
    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. Hannart, Alexis & Naveau, Philippe, 2014. "Estimating high dimensional covariance matrices: A new look at the Gaussian conjugate framework," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 149-162.
    2. Weilong Liu & Yanchu Liu, 2025. "Covariance Matrix Estimation for Positively Correlated Assets," Papers 2507.01545, arXiv.org.
    3. Avagyan, Vahe & Alonso Fernández, Andrés Modesto & Nogales, Francisco J., 2015. "D-trace Precision Matrix Estimation Using Adaptive Lasso Penalties," DES - Working Papers. Statistics and Econometrics. WS 21775, Universidad Carlos III de Madrid. Departamento de Estadística.
    4. Mishra, Anil V., 2016. "Foreign bias in Australian-domiciled mutual fund holdings," Pacific-Basin Finance Journal, Elsevier, vol. 39(C), pages 101-123.
    5. McDowell, Shaun, 2018. "An empirical evaluation of estimation error reduction strategies applied to international diversification," Journal of Multinational Financial Management, Elsevier, vol. 44(C), pages 1-13.
    6. Bagnara, Matteo & Vaucher, Benoit, 2025. "Risk diversification and extreme risk mitigation," Journal of Empirical Finance, Elsevier, vol. 83(C).
    7. Olivier Ledoit & Michael Wolf, 2003. "Honey, I shrunk the sample covariance matrix," Economics Working Papers 691, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Konno, Yoshihiko, 2009. "Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2237-2253, November.
    9. Wessel N. Wieringen & Gwenaël G. R. Leday, 2024. "Ridge-type covariance and precision matrix estimators of the multivariate normal distribution," Statistical Papers, Springer, vol. 65(9), pages 5835-5849, December.
    10. Yuan, Ke-Hai & Chan, Wai, 2008. "Structural equation modeling with near singular covariance matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4842-4858, June.
    11. Jian Zhang & Li Su, 2015. "Temporal Autocorrelation-Based Beamforming With MEG Neuroimaging Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1375-1388, December.
    12. Marie Diekmann & Ludwig Theuvsen, 2019. "Value structures determining community supported agriculture: insights from Germany," Agriculture and Human Values, Springer;The Agriculture, Food, & Human Values Society (AFHVS), vol. 36(4), pages 733-746, December.
    13. MohammadAmin Fazli & Parsa Alian & Ali Owfi & Erfan Loghmani, 2021. "RPS: Portfolio Asset Selection using Graph based Representation Learning," Papers 2111.15634, arXiv.org.
    14. Pesaran, M. Hashem & Yamagata, Takashi, 2012. "Testing CAPM with a Large Number of Assets," IZA Discussion Papers 6469, IZA Network @ LISER.
    15. Füss, Roland & Miebs, Felix & Trübenbach, Fabian, 2014. "A jackknife-type estimator for portfolio revision," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 14-28.
    16. Christian Bongiorno, 2020. "Bootstraps Regularize Singular Correlation Matrices," Working Papers hal-02536278, HAL.
    17. Emmanuelle Jay & Thibault Soler & Eugénie Terreaux & Jean-Philippe Ovarlez & Frédéric Pascal & Philippe de Peretti & Christophe Chorro, 2020. "Improving portfolios global performance using a cleaned and robust covariance matrix estimate," Post-Print hal-02508748, HAL.
    18. Wessel N. van Wieringen & Carel F. W. Peeters & Renee X. de Menezes & Mark A. van de Wiel, 2018. "Testing for pathway (in)activation by using Gaussian graphical models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1419-1436, November.
    19. Ali Atiah Alzahrani, 2025. "Multi-Agent Regime-Conditioned Diffusion (MARCD) for CVaR-Constrained Portfolio Decisions," Papers 2510.10807, arXiv.org, revised Nov 2025.
    20. Arbia, Giuseppe & Bramante, Riccardo & Facchinetti, Silvia & Zappa, Diego, 2018. "Modeling inter-country spatial financial interactions with Graphical Lasso: An application to sovereign co-risk evaluation," Regional Science and Urban Economics, Elsevier, vol. 70(C), pages 72-79.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:vrs:offsta:v:39:y:2023:i:4:p:459-487:n:2. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.