IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v154y2017icp112-134.html
   My bibliography  Save this article

Nonparametric estimation of a latent variable model

Author

Listed:
  • Kelava, Augustin
  • Kohler, Michael
  • Krzyżak, Adam
  • Schaffland, Tim Fabian

Abstract

In this paper a nonparametric latent variable model is estimated without specifying the underlying distributions. The main idea is to estimate in a first step a common factor analysis model under the assumption that each manifest variable is influenced by at most one of the latent variables. In a second step nonparametric regression is used to analyze the relation between the latent variables. Theoretical results concerning consistency of the estimates are presented, and the finite sample size performance of the estimates is illustrated by applying them to simulated data.

Suggested Citation

  • Kelava, Augustin & Kohler, Michael & Krzyżak, Adam & Schaffland, Tim Fabian, 2017. "Nonparametric estimation of a latent variable model," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 112-134.
    • Handle: RePEc:eee:jmvana:v:154:y:2017:i:c:p:112-134
    DOI: 10.1016/j.jmva.2016.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X1630118X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.10.006?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. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. C. Vale & Vincent Maurelli, 1983. "Simulating multivariate nonnormal distributions," Psychometrika, Springer;The Psychometric Society, vol. 48(3), pages 465-471, September.
    3. Zhao, L. C., 1987. "Exponential bounds of mean error for the nearest neighbor estimates of regression functions," Journal of Multivariate Analysis, Elsevier, vol. 21(1), pages 168-178, February.
    4. Irina Irincheeva & Eva Cantoni & Marc G. Genton, 2012. "Generalized Linear Latent Variable Models with Flexible Distribution of Latent Variables," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(4), pages 663-680, December.
    5. Francesco Bartolucci, 2006. "Likelihood inference for a class of latent Markov models under linear hypotheses on the transition probabilities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 155-178, April.
    6. Conne, David & Ronchetti, Elvezio & Victoria-Feser, Maria-Pia, 2010. "Goodness of Fit for Generalized Linear Latent Variables Models," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1126-1134.
    7. Bai, Jushan & Ng, Serena, 2006. "Evaluating latent and observed factors in macroeconomics and finance," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 507-537.
    8. Francesco Bartolucci & Fulvia Pennoni & Brian Francis, 2007. "A latent Markov model for detecting patterns of criminal activity," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(1), pages 115-132, January.
    9. Joseph Kruskal, 1976. "More factors than subjects, tests and treatments: An indeterminacy theorem for canonical decomposition and individual differences scaling," Psychometrika, Springer;The Psychometric Society, vol. 41(3), pages 281-293, September.
    10. Breslaw, Jon A. & McIntosh, James, 1998. "Simulated latent variable estimation of models with ordered categorical data," Journal of Econometrics, Elsevier, vol. 87(1), pages 25-47, August.
    11. Andreas Klein & Helfried Moosbrugger, 2000. "Maximum likelihood estimation of latent interaction effects with the LMS method," Psychometrika, Springer;The Psychometric Society, vol. 65(4), pages 457-474, December.
    12. Peter Hall & Hans‐Georg Müller & Fang Yao, 2008. "Modelling sparse generalized longitudinal observations with latent Gaussian processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(4), pages 703-723, September.
    13. R. Jennrich & P. Sampson, 1966. "Rotation for simple loadings," Psychometrika, Springer;The Psychometric Society, vol. 31(3), pages 313-323, September.
    14. Anderson, T. W., 1989. "Linear latent variable models and covariance structures," Journal of Econometrics, Elsevier, vol. 41(1), pages 91-119, May.
    15. Li, Tong, 2002. "Robust and consistent estimation of nonlinear errors-in-variables models," Journal of Econometrics, Elsevier, vol. 110(1), pages 1-26, September.
    16. Bianconcini, Silvia & Cagnone, Silvia, 2012. "Estimation of generalized linear latent variable models via fully exponential Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 183-193.
    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. Kim, Hyun Hak & Swanson, Norman R., 2018. "Mining big data using parsimonious factor, machine learning, variable selection and shrinkage methods," International Journal of Forecasting, Elsevier, vol. 34(2), pages 339-354.
    2. Chen, Liang, 2012. "Identifying observed factors in approximate factor models: estimation and hypothesis testing," MPRA Paper 37514, University Library of Munich, Germany.
    3. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    4. Bianco, Dominique & Niang, Abdou-Aziz, 2012. "On international spillovers," Economics Letters, Elsevier, vol. 117(1), pages 280-282.
    5. Francesco Bartolucci & Ivonne Solis-Trapala, 2010. "Multidimensional Latent Markov Models in a Developmental Study of Inhibitory Control and Attentional Flexibility in Early Childhood," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 725-743, December.
    6. Nii Ayi Armah & Norman Swanson, 2010. "Seeing Inside the Black Box: Using Diffusion Index Methodology to Construct Factor Proxies in Large Scale Macroeconomic Time Series Environments," Econometric Reviews, Taylor & Francis Journals, vol. 29(5-6), pages 476-510.
    7. Cathy Chen & Wolfgang Härdle, 2015. "Common factors in credit defaults swap markets," Computational Statistics, Springer, vol. 30(3), pages 845-863, September.
    8. Issler, João Victor & Lima, Luiz Renato, 2009. "A panel data approach to economic forecasting: The bias-corrected average forecast," Journal of Econometrics, Elsevier, vol. 152(2), pages 153-164, October.
    9. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    10. Sandra Eickmeier & Boris Hofmann, 2022. "What drives inflation? Disentangling demand and supply factors," BIS Working Papers 1047, Bank for International Settlements.
    11. Goyal, Amit & Pérignon, Christophe & Villa, Christophe, 2008. "How common are common return factors across the NYSE and Nasdaq?," Journal of Financial Economics, Elsevier, vol. 90(3), pages 252-271, December.
    12. Nii Ayi Armah & Norman Swanson, 2011. "Some variables are more worthy than others: new diffusion index evidence on the monitoring of key economic indicators," Applied Financial Economics, Taylor & Francis Journals, vol. 21(1-2), pages 43-60.
    13. Herrerias, M.J. & Ordoñez, J., 2012. "New evidence on the role of regional clusters and convergence in China (1952–2008)," China Economic Review, Elsevier, vol. 23(4), pages 1120-1133.
    14. Norman R. Swanson, 2016. "Comment," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(3), pages 348-353, July.
    15. Norman R. Swanson & Weiqi Xiong & Xiye Yang, 2020. "Predicting interest rates using shrinkage methods, real‐time diffusion indexes, and model combinations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(5), pages 587-613, August.
    16. Brownlees, Christian & Mesters, Geert, 2021. "Detecting granular time series in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 544-561.
    17. Peter C. B. Phillips & Donggyu Sul, 2007. "Transition Modeling and Econometric Convergence Tests," Econometrica, Econometric Society, vol. 75(6), pages 1771-1855, November.
    18. Castagnetti, Carolina & Rossi, Eduardo & Trapani, Lorenzo, 2019. "A two-stage estimator for heterogeneous panel models with common factors," Econometrics and Statistics, Elsevier, vol. 11(C), pages 63-82.
    19. Eric Bataille & Catherine Bruneau & Frederic Michaud, 2007. "Business cycle and corporate failure in France: Is there a link?," Computational Economics, Springer;Society for Computational Economics, vol. 29(2), pages 173-197, March.
    20. Alain-Philippe Fortin & Patrick Gagliardini & Olivier Scaillet, 2023. "Latent Factor Analysis in Short Panels," Papers 2306.14004, arXiv.org, revised May 2024.

    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:jmvana:v:154:y:2017:i:c:p:112-134. 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.