IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v85y2023i1d10.1007_s13171-021-00250-7.html
   My bibliography  Save this article

Behaviour of the Monotone Single Index Model Under Repeated Measurements

Author

Listed:
  • Fadoua Balabdaoui

    (Seminar for Statistics, ETH Zürich)

  • Cécile Durot

    (Modal’x, Université Paris Nanterre)

  • Hanna Jankowski

    (York University)

Abstract

The generalized linear model is an important method in the statistical toolkit. The isotonic single index model can be thought of as a further generalization whereby the link function is assumed to be monotone non-decreasing as opposed to known and fixed. Such a shape constraint is quite natural in many statistical problems, and is fulfilled by the usual generalized linear models. In this paper we consider inference in this model in the setting where repeated measurements of predictor values and associated responses are observed. This setting is encountered in medical studies and is very different from the one considered in the classical monotone single index model studied in the literature. Here, we use nonparametric maximum likelihood estimation to infer the unknown regression vector and link function. We present a detailed study of finite and asymptotic properties of this estimator and propose goodness-of-fit tests for the model. Through an extended simulation study, we show that the model has competitive predictive performance. We illustrate our estimation approach using a Leukemia data set.

Suggested Citation

  • Fadoua Balabdaoui & Cécile Durot & Hanna Jankowski, 2023. "Behaviour of the Monotone Single Index Model Under Repeated Measurements," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 324-350, February.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00250-7
    DOI: 10.1007/s13171-021-00250-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-021-00250-7
    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/s13171-021-00250-7?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. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    2. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
    3. Yining Chen & Richard J. Samworth, 2016. "Generalized additive and index models with shape constraints," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(4), pages 729-754, September.
    4. Hayfield, Tristen & Racine, Jeffrey S., 2008. "Nonparametric Econometrics: The np Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 27(i05).
    5. Maiying Kong & J. Jack Lee, 2006. "A Generalized Response Surface Model with Varying Relative Potency for Assessing Drug Interaction," Biometrics, The International Biometric Society, vol. 62(4), pages 986-995, December.
    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. Frölich, Markus & Huber, Martin & Wiesenfarth, Manuel, 2017. "The finite sample performance of semi- and non-parametric estimators for treatment effects and policy evaluation," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 91-102.
    2. Philippe Polomé, 2013. "Mimic Behavior in Home Waste-waters Management," Working Papers halshs-00855051, HAL.
    3. Eozenou, Patrick, 2008. "The Determinants of Private Transfers in Rural Vietnam," MPRA Paper 12773, University Library of Munich, Germany.
    4. Steven F. Koch, 2022. "Equivalence scales in a developing country with extensive inequality," South African Journal of Economics, Economic Society of South Africa, vol. 90(4), pages 486-512, December.
    5. Ardakani, Omid M. & Kishor, N. Kundan & Song, Suyong, 2018. "Re-evaluating the effectiveness of inflation targeting," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 76-97.
    6. Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," Papers 1811.03329, arXiv.org, revised Jan 2020.
    7. Philippe Polomé, 2013. "Limited higher order beliefs and the welfare effects of public information," Working Papers 1325, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    8. Arulampalam, Wiji & Corradi, Valentina & Gutknecht, Daniel, 2021. "Intercept Estimation in Nonlinear Selection Models," IZA Discussion Papers 14364, Institute of Labor Economics (IZA).
    9. Ardakani, Omid & Kishor, Kundan & Song, Suyong, 2015. "On the Effectiveness of Inflation Targeting: Evidence from a Semiparametric Approach," MPRA Paper 75091, University Library of Munich, Germany.
    10. Chu-Ping C. Vijverberg & Wim P. M. Vijverberg, 2016. "Pregibit: a family of binary choice models," Empirical Economics, Springer, vol. 50(3), pages 901-932, May.
    11. Ranjeeta Thomas, 2012. "Conditional Cash Transfers To Improve Education And Health: An Ex Ante Evaluation Of Red De Protección Social, Nicaragua," Health Economics, John Wiley & Sons, Ltd., vol. 21(10), pages 1136-1154, October.
    12. Jiaying Gu & Roger Koenker, 2018. "Nonparametric maximum likelihood methods for binary response models with random coefficients," CeMMAP working papers CWP65/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    13. David H. Bernstein & Christopher F. Parmeter, 2017. "Returns to Scale in Electricity Generation: Revisited and Replicated," Working Papers 2017-08, University of Miami, Department of Economics.
    14. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    15. Bodory, Hugo & Huber, Martin, 2018. "The causalweight package for causal inference in R," FSES Working Papers 493, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    16. Bucher, Axel & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Single-index quantile regression models for censored data," LIDAM Discussion Papers ISBA 2014001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Park, Byeong U. & Simar, Léopold & Zelenyuk, Valentin, 2017. "Nonparametric estimation of dynamic discrete choice models for time series data," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 97-120.
    18. Besstremyannaya, Galina, 2015. "Measuring the effect of health insurance companies on the quality of healthcare systems with kernel and parametric regressions," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 3-20.
    19. Michael S. Delgado & Daniel J. Henderson & Christopher F. Parmeter, 2014. "Does Education Matter for Economic Growth?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(3), pages 334-359, June.
    20. Mittelhammer, Ron C. & Judge, George, 2011. "A family of empirical likelihood functions and estimators for the binary response model," Journal of Econometrics, Elsevier, vol. 164(2), pages 207-217, October.

    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:sankha:v:85:y:2023:i:1:d:10.1007_s13171-021-00250-7. 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.