IDEAS home Printed from https://ideas.repec.org/p/cir/cirwor/2011s-57.html
   My bibliography  Save this paper

Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes

Author

Listed:
  • John W. Galbraith
  • Victoria Zinde-Walsh

Abstract

Regression models sometimes contain a linear parametric part and a part obtained by reducing the dimension of a larger set of data. This paper considers properties of estimates of the interpretable parameters of the model, in a general setting in which a potentially unbounded set of other variables may be relevant, and where the number of included factors or components representing these variables can also grow without bound as sample size increases. We show that consistent (and asymptotically normal, given further restrictions) estimation of a parameter of interest is possible in this setting. We examine selection of the particular orthogonal directions, using a criterion which takes into account both the magnitude of the eigenvalue and the correlation of the eigenvector with the variable of interest. Simulation experiments show that an implementation of this method may have good finite-sample performance.

Suggested Citation

  • John W. Galbraith & Victoria Zinde-Walsh, 2011. "Partially Dimension-Reduced Regressions with Potentially Infinite-Dimensional Processes," CIRANO Working Papers 2011s-57, CIRANO.
    • Handle: RePEc:cir:cirwor:2011s-57
    as

    Download full text from publisher

    File URL: https://cirano.qc.ca/files/publications/2011s-57.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    2. Alexandre Belloni & Victor Chernozhukov, 2009. "L1-Penalized Quantile Regression in High-Dimensional Sparse Models," Papers 0904.2931, arXiv.org, revised Sep 2019.
    3. Forni, Mario & Lippi, Marco, 2001. "The Generalized Dynamic Factor Model: Representation Theory," Econometric Theory, Cambridge University Press, vol. 17(6), pages 1113-1141, December.
    4. Magnus, Jan R. & Powell, Owen & Prüfer, Patricia, 2010. "A comparison of two model averaging techniques with an application to growth empirics," Journal of Econometrics, Elsevier, vol. 154(2), pages 139-153, February.
    5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    6. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    7. Jan R. Magnus & J. Durbin, 1999. "Estimation of Regression Coefficients of Interest When Other Regression Coefficients Are of No Interest," Econometrica, Econometric Society, vol. 67(3), pages 639-644, May.
    8. Zernov, Serguei & Zinde-Walsh, Victoria & Galbraith, John W., 2009. "Asymptotics for estimation of quantile regressions with truncated infinite-dimensional processes," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 497-508, March.
    9. Jan J. J. Groen & George Kapetanios, 2009. "Model selection criteria for factor-augmented regressions," Staff Reports 363, Federal Reserve Bank of New York.
    10. Magnus, J.R. & Powell, O.R. & Prüfer, P., 2008. "A Comparison of Two Averaging Techniques with an Application to Growth Empirics," Other publications TiSEM 0392dffa-51e0-4bc9-9644-f, Tilburg University, School of Economics and Management.
    11. Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-1304, September.
    12. Farebrother, R W, 1972. "Principal Component Estimators and Minimum Mean Square Error Criteria in Regression Analysis," The Review of Economics and Statistics, MIT Press, vol. 54(3), pages 332-336, 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. Galbraith, John W. & Hodgson, Douglas J., 2012. "Dimension reduction and model averaging for estimation of artists' age-valuation profiles," European Economic Review, Elsevier, vol. 56(3), pages 422-435.
    2. John Galbraith & Douglas Hodgson, 2015. "Innovation, experience and artists’ age-valuation profiles: evidence from eighteenth-century rococo and neoclassical painters," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 39(3), pages 259-275, August.

    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. Galbraith, John W. & Zinde-Walsh, Victoria, 2020. "Simple and reliable estimators of coefficients of interest in a model with high-dimensional confounding effects," Journal of Econometrics, Elsevier, vol. 218(2), pages 609-632.
    2. Helmut Lütkepohl, 2014. "Structural Vector Autoregressive Analysis in a Data Rich Environment: A Survey," Discussion Papers of DIW Berlin 1351, DIW Berlin, German Institute for Economic Research.
    3. Smeekes, Stephan & Wijler, Etienne, 2018. "Macroeconomic forecasting using penalized regression methods," International Journal of Forecasting, Elsevier, vol. 34(3), pages 408-430.
    4. Mario Forni & Luca Gambetti & Luca Sala, 2014. "No News in Business Cycles," Economic Journal, Royal Economic Society, vol. 124(581), pages 1168-1191, December.
    5. Tomohiro Ando & Ruey S. Tsay, 2009. "Model selection for generalized linear models with factor‐augmented predictors," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 207-235, May.
    6. Jan R. Magnus & Wendun Wang & Xinyu Zhang, 2016. "Weighted-Average Least Squares Prediction," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 1040-1074, June.
    7. Forni, Mario & Hallin, Marc & Lippi, Marco & Reichlin, Lucrezia, 2005. "The Generalized Dynamic Factor Model: One-Sided Estimation and Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 830-840, September.
    8. Matteo Luciani & David Veredas, 2012. "A model for vast panels of volatilities," Working Papers 1230, Banco de España.
    9. Matteo Barigozzi & Antonio M. Conti & Matteo Luciani, 2014. "Do Euro Area Countries Respond Asymmetrically to the Common Monetary Policy?," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(5), pages 693-714, October.
    10. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    11. Norman R. Swanson & Weiqi Xiong, 2018. "Big data analytics in economics: What have we learned so far, and where should we go from here?," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 51(3), pages 695-746, August.
    12. Massacci, Daniele, 2017. "Least squares estimation of large dimensional threshold factor models," Journal of Econometrics, Elsevier, vol. 197(1), pages 101-129.
    13. Pellényi, Gábor, 2012. "A monetáris politika hatása a magyar gazdaságra. Elemzés strukturális, dinamikus faktormodellel [The sectoral effects of monetary policy in Hungary: a structural factor]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(3), pages 263-284.
    14. Bai, Jushan & Ando, Tomohiro, 2013. "Multifactor asset pricing with a large number of observable risk factors and unobservable common and group-specific factors," MPRA Paper 52785, University Library of Munich, Germany, revised Dec 2013.
    15. Jushan Bai & Serena Ng, 2020. "Simpler Proofs for Approximate Factor Models of Large Dimensions," Papers 2008.00254, arXiv.org.
    16. Hagen, Tobias, 2013. "Impact of national financial regulation on macroeconomic and fiscal performance after the 2007 financial stock: Econometric analyses based on cross-country data," Working Paper Series 02, Frankfurt University of Applied Sciences, Faculty of Business and Law.
    17. Matteo Barigozzi & Marc Hallin, 2023. "Dynamic Factor Models: a Genealogy," Papers 2310.17278, arXiv.org, revised Jan 2024.
    18. Banerjee, Anindya & Marcellino, Massimiliano & Masten, Igor, 2014. "Forecasting with factor-augmented error correction models," International Journal of Forecasting, Elsevier, vol. 30(3), pages 589-612.
    19. Matteo Barigozzi & Marc Hallin, 2016. "Generalized dynamic factor models and volatilities: recovering the market volatility shocks," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 33-60, February.
    20. Mario Forni & Luca Gambetti, 2010. "Macroeconomic Shocks and the Business Cycle: Evidence from a Structural Factor Model," Center for Economic Research (RECent) 040, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".

    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:cir:cirwor:2011s-57. 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: Webmaster (email available below). General contact details of provider: https://edirc.repec.org/data/ciranca.html .

    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.