Advanced Search
MyIDEAS: Login

Feasible Multivariate Nonparametric Estimation Using Weak Separability

Contents:

Author Info

  • Joris Pinkse

    (University of British Columbia)

Registered author(s):

    Abstract

    One of the main practical problems of nonparametric regression estimation is the curse of dimensionality. The curse of dimensionality arises because nonparametric regression estimates are dependent variable averages local to the point at which the regression function is to be estimated. The number of observations `local' to the point of estimation decreases exponentially with the number of dimensions. The consequence is that the variance of unconstrained nonparametric regression estimators of multivariate regression functions is often so great that the unconstrained nonparametric regression estimates are of no practical use. In this paper I propose a new estimation method of weakly separable multivariate nonparametric regression functions. Weak separability is a weaker condition than required by other dimension--reduction techniques, although similar asymptotic variance reductions obtain. Indeed, weak separability is weaker than generalized additivity (see Hardle and Linton, 1996 and Horowitz, 1998). The proposed estimator is relatively easy to compute. Theoretical results in this paper include (i) a uniform law of large numbers for marginal integration estimators, (ii) a uniform law of large numbers for marginal summation estimators, (iii) a uniform law of large numbers for my new nonparametric regression estimator for weakly separable regression functions, (iv) both a uniform strong and weak law of large numbers for U-statistics, and (v) three central limit theorems for my nonparametric regression estimator for weakly separable regression functions.

    Download Info

    If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
    File URL: http://fmwww.bc.edu/RePEc/es2000/1241.pdf
    File Function: main text
    Download Restriction: no

    Bibliographic Info

    Paper provided by Econometric Society in its series Econometric Society World Congress 2000 Contributed Papers with number 1241.

    as in new window
    Length:
    Date of creation: 01 Aug 2000
    Date of revision:
    Handle: RePEc:ecm:wc2000:1241

    Contact details of provider:
    Phone: 1 212 998 3820
    Fax: 1 212 995 4487
    Email:
    Web page: http://www.econometricsociety.org/pastmeetings.asp
    More information through EDIRC

    Related research

    Keywords:

    References

    References listed on IDEAS
    Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
    as in new window
    1. Blundell, Richard, 1988. "Consumer Behaviour: Theory and Empirical Evidence--a Survey," Economic Journal, Royal Economic Society, vol. 98(389), pages 16-65, March.
    2. 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.
    3. Woodland, Alan D., 1978. "On testing weak separability," Journal of Econometrics, Elsevier, vol. 8(3), pages 383-398, December.
    4. Blackorby, Charles & Davidson, Russell & Schworm, William, 1991. "Implicit separability: Characterisation and implications for consumer demands," Journal of Economic Theory, Elsevier, vol. 55(2), pages 364-399, December.
    5. Horowitz, J.L., 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Working Papers 98-05, University of Iowa, Department of Economics.
    6. J. Horowitz, 1998. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," SFB 373 Discussion Papers 1998,83, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    7. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
    8. repec:wop:humbsf:1998-83 is not listed on IDEAS
    9. Donald W.K. Andrews, 1988. "Asymptotic Normality of Series Estimators for Nonparametric and Semiparametric Regression Models," Cowles Foundation Discussion Papers 874R, Cowles Foundation for Research in Economics, Yale University, revised May 1989.
    10. BLACKORBY, Ch. & SCHWORM, W. & FISHER, T., 1986. "Testing for the existence of input aggregates in an economy production function," CORE Discussion Papers 1986046, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. William Barnett, 2005. "Monetary Aggregation," Macroeconomics 0503017, EconWPA.
    12. Rilstone, Paul, 1996. "Nonparametric Estimation of Models with Generated Regressors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 37(2), pages 299-313, May.
    13. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    14. 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 675-83, May.
    15. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    16. Newey, W.K., 1989. "Uniform Convergence In Probability And Stochastic Equicontinuity," Papers 342, Princeton, Department of Economics - Econometric Research Program.
    17. Oliver Linton & Pedro Gozalo, 1995. "Testing Additivity in Generalized Nonparametric Regression Models," Cowles Foundation Discussion Papers 1106, Cowles Foundation for Research in Economics, Yale University.
    18. Delgado, Miguel A & Mora, Juan, 1995. "Nonparametric and Semiparametric Estimation with Discrete Regressors," Econometrica, Econometric Society, vol. 63(6), pages 1477-84, November.
    19. Gozalo, Pedro L., 1993. "A Consistent Model Specification Test for Nonparametric Estimation of Regression Function Models," Econometric Theory, Cambridge University Press, vol. 9(03), pages 451-477, June.
    20. Ahn, Hyungtaik, 1997. "Semiparametric Estimation of a Single-Index Model with Nonparametrically Generated Regressors," Econometric Theory, Cambridge University Press, vol. 13(01), pages 3-31, February.
    21. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
    22. Diewert, W E & Wales, T J, 1988. "Normalized Quadratic Systems of Consumer Demand Functions," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(3), pages 303-12, July.
    23. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    24. Blackorby, Charles & Schworm, William, 1988. "The Existence of Input and Output Aggregates in Aggregate Production Functions," Econometrica, Econometric Society, vol. 56(3), pages 613-43, May.
    25. Richard Blundell & Jean-Marc Robin, 2000. "Latent Separability: Grouping Goods without Weak Separability," Econometrica, Econometric Society, vol. 68(1), pages 53-84, January.
    26. Diewert, W. E. & Wales, T. J., 1995. "Flexible functional forms and tests of homogeneous separability," Journal of Econometrics, Elsevier, vol. 67(2), pages 259-302, June.
    27. Fan, Yanqin & Li, Qi, 1996. "Consistent Model Specification Tests: Omitted Variables and Semiparametric Functional Forms," Econometrica, Econometric Society, vol. 64(4), pages 865-90, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Lists

    This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

    Statistics

    Access and download statistics

    Corrections

    When requesting a correction, please mention this item's handle: RePEc:ecm:wc2000:1241. 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: (Christopher F. Baum).

    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 references are entirely missing, you can add them using this form.

    If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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