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A Simple Ordered Data Estimator For Inverse Density Weighted Functions

  • Arthur Lewbel

    ()

    (Boston College)

  • Susanne M. Schennach

    (University of Chicago)

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The "ordered data" estimator we provide is root n consistent, asymptotically normal, and is numerically extremely simple, involving little more than ordering the data and summing the results. No sample size dependent smoothing is required. A similarly simple estimator is provided for the limiting variance. The proofs include new limiting distribution results for functions of nearest neighbor spacings. Potential applications include endogeneous binary choice, willingness to pay, selection, and treatment models.

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Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 557.

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Length: 27 pages
Date of creation: 04 Apr 2003
Date of revision: 01 May 2005
Publication status: forthcoming, Journal of Econometrics
Handle: RePEc:boc:bocoec:557
Note: Previously circulated as "A Simple Ordered Data Estimator for Inverse Density Weighted Expectations"
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Web page: http://fmwww.bc.edu/EC/Email:


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  1. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, 07.
  2. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
  3. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  4. Newey, W.K., 1989. "The Asymptotic Variance Of Semiparametric Estimotors," Papers 346, Princeton, Department of Economics - Econometric Research Program.
  5. Arthur Lewbel, 1998. "Semiparametric Latent Variable Model Estimation with Endogenous or Mismeasured Regressors," Econometrica, Econometric Society, vol. 66(1), pages 105-122, January.
  6. Yongmiao Hong & Halbert White, 2005. "Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence," Econometrica, Econometric Society, vol. 73(3), pages 837-901, 05.
  7. Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
  8. Arthur Lewbel, 2000. "Endogenous Selection Or Treatment Model Estimation," Boston College Working Papers in Economics 462, Boston College Department of Economics, revised 13 Jun 2007.
  9. Barbe, Philippe, 1994. "Joint approximation of processes based on spacings and order statistics," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 339-349, October.
  10. Arthur Lewbel & Daniel McFadden & Oliver Linton, 1997. "Estimating Features of a Distribution from Binomial Data," Boston College Working Papers in Economics 442, Boston College Department of Economics, revised 01 Jul 2010.
  11. Magnac, Thierry & Maurin, Eric, 2007. "Identification and information in monotone binary models," Journal of Econometrics, Elsevier, vol. 139(1), pages 76-104, July.
  12. Mack, Y. P. & Müller, Hans-Georg, 1988. "Convolution type estimators for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 229-239, December.
  13. Denis Cogneau & Eric Maurin, 2001. "Parental Income and School Attendance in a Low-Income Country : A Semi-parametric Analysis," Working Papers 2001-08, Centre de Recherche en Economie et Statistique.
  14. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February.
  15. Whitney K. Newey and Paul A. Ruud., 1994. "Density Weighted Linear Least Squares," Economics Working Papers 94-228, University of California at Berkeley.
  16. Daniel McFadden, 1996. "Computing Willingness-to-Pay in Random Utility Models," Working Papers _011, University of California at Berkeley, Econometrics Laboratory Software Archive.
  17. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.
  18. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
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