IDEAS home Printed from https://ideas.repec.org/p/nbr/nberte/0085.html
   My bibliography  Save this paper

On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach

Author

Listed:
  • Benedikt M. Potscher
  • Ingmar R. Prucha

Abstract

The paper develops a general framework for the formulation of generic uniform laws of large numbers. In particular, we introduce a basic generic uniform law of large numbers that contains recent uniform laws of large numbers by Andrews [2] and Hoadley [7J as special cases. We also develop a truncation approach .that makes it possible to obtain uniform laws of large numbers for the functions under consideration from uniform laws of large numbers for truncated versions of those functions. The point of the truncation approach is that uniform laws of large numbers for the truncated versions are typically easier to obtain. By combining the basic uniform law of large numbers and the truncation approach we also derive generalizations of recent uniform laws of large numbers introduced in Potscher and Prucha [13, l5].

Suggested Citation

  • Benedikt M. Potscher & Ingmar R. Prucha, 1994. "On the Formulation of Uniform Laws of Large Numbers: A Truncation Approach," NBER Technical Working Papers 0085, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0085
    Note: PR
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/t0085.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Levine, David, 1983. "A remark on serial correlation in maximum likelihood," Journal of Econometrics, Elsevier, vol. 23(3), pages 337-342, December.
    2. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    3. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    4. Bates, Charles & White, Halbert, 1985. "A Unified Theory of Consistent Estimation for Parametric Models," Econometric Theory, Cambridge University Press, vol. 1(2), pages 151-178, August.
    5. Potscher, Benedikt M & Prucha, Ingmar R, 1989. "A Uniform Law of Large Numbers for Dependent and Heterogeneous Data Processes," Econometrica, Econometric Society, vol. 57(3), pages 675-683, May.
    6. White, Halbert, 1980. "Nonlinear Regression on Cross-Section Data," Econometrica, Econometric Society, vol. 48(3), pages 721-746, April.
    7. Donald W.K. Andrews, 1986. "Consistency in Nonlinear Econometric Models: A Generic Uniform Law of Large Numbers," Cowles Foundation Discussion Papers 790, Cowles Foundation for Research in Economics, Yale University.
    8. Domowitz, Ian & White, Halbert, 1982. "Misspecified models with dependent observations," Journal of Econometrics, Elsevier, vol. 20(1), pages 35-58, October.
    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. Jenish, Nazgul & Prucha, Ingmar R., 2009. "Central limit theorems and uniform laws of large numbers for arrays of random fields," Journal of Econometrics, Elsevier, vol. 150(1), pages 86-98, May.

    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. Ian Domowitz, 1985. "New Directions in Non-linear Estimation with Dependent Observations," Canadian Journal of Economics, Canadian Economics Association, vol. 18(1), pages 1-27, February.
    2. Andrews, Donald W. K. & Fair, Ray C., 1987. "Inference in Econometric Models with Structural Change," Working Papers 636, California Institute of Technology, Division of the Humanities and Social Sciences.
    3. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    4. Jeffrey M. Woodridge, 1988. "A Unified Approach to Robust, Regression-Based Specification Tests," Working papers 480, Massachusetts Institute of Technology (MIT), Department of Economics.
    5. Calzolari, Giorgio, 1992. "Stima delle equazioni simultanee non-lineari: una rassegna [Estimation of nonlinear simultaneous equations: a survey]," MPRA Paper 24123, University Library of Munich, Germany, revised 1992.
    6. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
    7. de Jong, Robert M., 1998. "Uniform laws of large numbers and stochastic Lipschitz-continuity," Journal of Econometrics, Elsevier, vol. 86(2), pages 243-268, June.
    8. Yongmiao Hong & Jin Lee, 2000. "Wavelet-based Estimation for Heteroskedasticity and Autocorrelation Consistent Variance-Covariance Matrices," Econometric Society World Congress 2000 Contributed Papers 1211, Econometric Society.
    9. Marmer, Vadim & Otsu, Taisuke, 2012. "Optimal comparison of misspecified moment restriction models under a chosen measure of fit," Journal of Econometrics, Elsevier, vol. 170(2), pages 538-550.
    10. Davide Viviano & Jelena Bradic, 2019. "Synthetic learner: model-free inference on treatments over time," Papers 1904.01490, arXiv.org.
    11. Arie Preminger & Uri Ben-zion & David Wettstein, 2007. "The extended switching regression model: allowing for multiple latent state variables," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 26(7), pages 457-473.
    12. Andreasen, Martin M. & Christensen, Bent Jesper, 2015. "The SR approach: A new estimation procedure for non-linear and non-Gaussian dynamic term structure models," Journal of Econometrics, Elsevier, vol. 184(2), pages 420-451.
    13. Gopal K. Basak & Arnab Bhattacharjee & Samarjit Das, 2018. "Causal ordering and inference on acyclic networks," Empirical Economics, Springer, vol. 55(1), pages 213-232, August.
    14. Russell Davidson & Victoria Zinde‐Walsh, 2017. "Advances in specification testing," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1595-1631, December.
    15. repec:ebl:ecbull:v:3:y:2005:i:29:p:1-10 is not listed on IDEAS
    16. Henry Brady, 1989. "Factor and ideal point analysis for interpersonally incomparable data," Psychometrika, Springer;The Psychometric Society, vol. 54(2), pages 181-202, June.
    17. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    18. Tim Bollerslev & Robert J. Hodrick, 1992. "Financial Market Efficiency Tests," NBER Working Papers 4108, National Bureau of Economic Research, Inc.
    19. Fair, Ray C & Shiller, Robert J, 1989. "The Informational Context of Ex Ante Forecasts," The Review of Economics and Statistics, MIT Press, vol. 71(2), pages 325-331, May.
    20. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    21. Dedi Rosadi & Shelton Peiris, 2014. "Second-order least-squares estimation for regression models with autocorrelated errors," Computational Statistics, Springer, vol. 29(5), pages 931-943, October.

    More about this item

    JEL classification:

    • C - Mathematical and Quantitative Methods

    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:nbr:nberte:0085. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    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: (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.