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Estimating features of a distribution from binomial data

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Author Info
Arthur Lewbel (Institute for Fiscal Studies and Boston College)
Oliver Linton () (Institute for Fiscal Studies and London School of Economics)
Daniel McFadden () (Institute for Fiscal Studies and University of California, Berkeley)

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Abstract

A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. One application is destructive duration analysis, where the process is censored at an observation test time. Another is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values placed by consumers on a public good such as endangered species. Sample consumers are asked whether they would vote for a referendum that would provide the good at a cost speci…ed by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem.

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Publisher Info
Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP07/01.

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Length: 32 pp.
Date of creation: Dec 2001
Date of revision:
Handle: RePEc:ifs:cemmap:07/01

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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.:
  1. Lewbel, Arthur, 1997. "Semiparametric Estimation of Location and Other Discrete Choice Moments," Econometric Theory, Cambridge University Press, vol. 13(01), pages 32-51, February. [Downloadable!]
  2. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November. [Downloadable!] (restricted)
  3. repec:cup:etheor:v:13:y:1997:i:1:p:32-51 is not listed on IDEAS
  4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January. [Downloadable!] (restricted)
  5. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March. [Downloadable!] (restricted)
  6. Wolfgang Hardle & Oliver Linton, 1994. "Applied Nonparametric Methods," Cowles Foundation Discussion Papers 1069, Cowles Foundation, Yale University. [Downloadable!]
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  7. Gozalo, Pedro & Linton, Oliver, 2000. "Local nonlinear least squares: Using parametric information in nonparametric regression," Journal of Econometrics, Elsevier, vol. 99(1), pages 63-106, November. [Downloadable!] (restricted)
  8. Sherman, Robert P, 1993. "The Limiting Distribution of the Maximum Rank Correlation Estimator," Econometrica, Econometric Society, vol. 61(1), pages 123-37, January. [Downloadable!] (restricted)
  9. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September. [Downloadable!] (restricted)
  10. 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. [Downloadable!] (restricted)
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  11. W. H"Ardle & O. Linton, . "Nonparametric Regression," Sonderforschungsbereich 373 1995-29, Humboldt Universitaet Berlin.
Full references

Cited by:
(explanations, 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.)

  1. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric estimation of homothetic and homothetically separable functions," CeMMAP working papers CWP14/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  2. Kim, Soo-Il, 2006. "Bias and Efficiency of Uniform Bid Design in Contingent Valuation," 2006 Annual meeting, July 23-26, Long Beach, CA 21335, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association). [Downloadable!]
  3. Mogens Fosgerau, 2004. "Investigating the distribution of the value of travel time savings," Urban/Regional 0411006, EconWPA. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!]
    Other versions:
  5. Bo E. Honore & Arthur Lewbel, 1998. "Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors," Boston College Working Papers in Economics 455, Boston College Department of Economics, revised 22 Sep 2001. [Downloadable!]
    Other versions:
  6. Mogens Fosgerau, 2005. "Specification Of A Model To Measure - The Value Of Travel Time Savings From Binomial Data," ERSA conference papers ersa05p77, European Regional Science Association. [Downloadable!]
    Other versions:
  7. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics. [Downloadable!]
    Other versions:
  8. Fosgerau, Mogens & Hjort, Katrine & Vincent Lyk-Jensen, Stéphanie, 2007. "An approach to the estimation of the distribution of marginal valuations from discrete choice data," MPRA Paper 3907, University Library of Munich, Germany. [Downloadable!]
  9. Arthur Lewbel, 2002. "Ordered Response Threshold Estimation," Boston College Working Papers in Economics 535, Boston College Department of Economics, revised 29 Oct 2003. [Downloadable!]
  10. Thierry Magnac & Eric Maurin, 2003. "Identification & Information in Monotone Binary Models," Research Unit Working Papers 0309, Laboratoire d'Economie Appliquee, INRA. [Downloadable!]
    Other versions:
  11. Arthur Lewbel & Susanne M. Schennach, 2003. "A Simple Ordered Data Estimator For Inverse Density Weighted Functions," Boston College Working Papers in Economics 557, Boston College Department of Economics, revised 01 May 2005. [Downloadable!]
  12. Arthur Lewbel & Oliver Linton, 2003. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Boston College Working Papers in Economics 585, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
    Other versions:
  13. Arthur Lewbel, 2006. "Modeling Heterogeneity," Boston College Working Papers in Economics 650, Boston College Department of Economics. [Downloadable!]
  14. Magnac, Thierry & Maurin, Eric, 2003. "Identification and Information in Monotone Binary Models," IDEI Working Papers 180, Institut d'Économie Industrielle (IDEI), Toulouse, revised Oct 2004. [Downloadable!]
    Other versions:
  15. Arthur Lewbel, 2005. "Simple Endogenous Binary Choice and Selection Panel Model Estimators," Boston College Working Papers in Economics 613, Boston College Department of Economics, revised 04 Sep 2006. [Downloadable!]
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