IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v174y2021ics0167715221000626.html
   My bibliography  Save this article

A goodness-of-fit test based on neural network sieve estimators

Author

Listed:
  • Shen, Xiaoxi
  • Jiang, Chang
  • Sakhanenko, Lyudmila
  • Lu, Qing

Abstract

Neural networks have become increasingly popular in the field of machine learning and have been successfully used in many applied fields (e.g., imaging recognition). With more and more research has been conducted on neural networks, we have a better understanding of the statistical proprieties of neural networks. While many studies focus on bounding the prediction error of neural network estimators, limited research has been done on the statistical inference of neural networks. From a statistical point of view, it is of great interest to investigate the statistical inference of neural networks as it could facilitate hypothesis testing in many fields (e.g., genetics, epidemiology, and medical science). In this paper, we propose a goodness-of-fit test statistic based on neural network sieve estimators. The test statistic follows an asymptotic distribution, which makes it easy to use in practice. We have also verified the theoretical asymptotic results via simulation studies and a real data application.

Suggested Citation

  • Shen, Xiaoxi & Jiang, Chang & Sakhanenko, Lyudmila & Lu, Qing, 2021. "A goodness-of-fit test based on neural network sieve estimators," Statistics & Probability Letters, Elsevier, vol. 174(C).
  • Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000626
    DOI: 10.1016/j.spl.2021.109100
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715221000626
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spl.2021.109100?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. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
    2. Yatchew, Adonis John, 1992. "Nonparametric Regression Tests Based on Least Squares," Econometric Theory, Cambridge University Press, vol. 8(4), pages 435-451, 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. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    2. Li, Qi & Hsiao, Cheng & Zinn, Joel, 2003. "Consistent specification tests for semiparametric/nonparametric models based on series estimation methods," Journal of Econometrics, Elsevier, vol. 112(2), pages 295-325, February.
    3. Yao Luo & Peijun Sang & Ruli Xiao, 2024. "Order Statistics Approaches to Unobserved Heterogeneity in Auctions," Working Papers tecipa-776, University of Toronto, Department of Economics.
    4. 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.
    5. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
    6. Chen, Xiaohong & Liao, Zhipeng & Sun, Yixiao, 2014. "Sieve inference on possibly misspecified semi-nonparametric time series models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 639-658.
    7. Temel, Tugrul T., 2001. "A Nonparametric Hypothesis Test Via The Bootstrap Resampling," 2001 Annual meeting, August 5-8, Chicago, IL 20600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Shiu, Ji-Liang & Hu, Yingyao, 2013. "Identification and estimation of nonlinear dynamic panel data models with unobserved covariates," Journal of Econometrics, Elsevier, vol. 175(2), pages 116-131.
    9. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    10. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    11. Brendstrup, Bjarne & Paarsch, Harry J., 2007. "Semiparametric identification and estimation in multi-object, English auctions," Journal of Econometrics, Elsevier, vol. 141(1), pages 84-108, November.
    12. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    13. Jungyoon Lee & Peter Robinson, 2016. "Series estimation under cross-sectional dependence," LSE Research Online Documents on Economics 63380, London School of Economics and Political Science, LSE Library.
    14. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2010. "Approximating the critical values of Cramér-von Mises tests in general parametric conditional specifications," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 625-636, March.
    15. Mammen, Enno & Rothe, Christoph & Schienle, Melanie, 2016. "Semiparametric Estimation With Generated Covariates," Econometric Theory, Cambridge University Press, vol. 32(5), pages 1140-1177, October.
    16. Horowitz, Joel L. & Spokoiny, Vladimir G., 1999. "An adaptive, rate-optimal test of a parametric model against a nonparametric alternative," SFB 373 Discussion Papers 1999,10, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    17. Chen, Liang & Pan, Haozi, 2023. "Estimation of characteristics-based quantile factor models," UC3M Working papers. Economics 37095, Universidad Carlos III de Madrid. Departamento de Economía.
    18. Xiaohong Chen & James J. Heckman & Edward Vytlacil, 2000. "Identification and SQRT N Efficient Estimation of Semiparametric Panel Data Models with Binary Dependent Variables and a Latent Factor," Econometric Society World Congress 2000 Contributed Papers 1567, Econometric Society.
    19. Michael Jansson & Demian Pouzo, 2017. "Towards a General Large Sample Theory for Regularized Estimators," Papers 1712.07248, arXiv.org, revised Jul 2020.
    20. Hong, Han & Mahajan, Aprajit & Nekipelov, Denis, 2015. "Extremum estimation and numerical derivatives," Journal of Econometrics, Elsevier, vol. 188(1), pages 250-263.

    More about this item

    Keywords

    Donsker class; Nonparametric least squares;

    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:eee:stapro:v:174:y:2021:i:c:s0167715221000626. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.