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Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data

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Author Info

  • Mark Yuying An

    (Duke Uniersity)

  • Roberto Ayala

    (Central Bank, Ecuador)

Abstract

In this paper we present a a generalized self-consistent algorithm that estimates a survivor function with across-interval- censored data. This algorithm is an iterative procedure based on Turnbull's (1974) reallocation idea. At each step of the iteration, the procedure first reduces the across-interval-censored problem to a singly-censored one, and then it applies the Kaplan-Meier estimation method. The main result of this paper is that our algorithm produces the maximum likelihood estimate. Unlike Turnbull (1974, 1976), we explicitly discuss situations in which corner solutions are encountered. The investigation is motivated from environmental economics where data from contingent valuation surveys are often used to nonparametrically estimate the willingness to pay distribution. In this estimation, the algorithm of Turnbull (1974, 1976) plays an instrumental role. However, there is a data grouping mechanism found in some contingent valuation surveys to which Turnbull's method does not apply. We refer to these cases as distinct bids and mixed bids, where across-interval-censored observations are common.

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Bibliographic Info

Paper provided by EconWPA in its series Econometrics with number 9611003.

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Length: 30 pages
Date of creation: 17 Nov 1996
Date of revision:
Handle: RePEc:wpa:wuwpem:9611003

Note: Type of Document - ; prepared on UNIX Sparc TeX; to print on PostScript; pages: 30 ; figures: request from author. We never published this piece and now we would like to reduce our mailing and xerox cost by posting it.
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Related research

Keywords: Across-Interval Censoring; Contingent valuation; Nonparametric Estimation; Self-Consistent Algorithm;

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References

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  1. Cameron, Trudy Ann & James, Michelle D, 1987. "Efficient Estimation Methods for "Closed-ended' Contingent Valuation Surveys," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 269-76, May.
  2. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, EconWPA.
  3. Carson, Richard T. & Hanemann, W. Michael, 2006. "Contingent Valuation," Handbook of Environmental Economics, in: K. G. Mäler & J. R. Vincent (ed.), Handbook of Environmental Economics, edition 1, volume 2, chapter 17, pages 821-936 Elsevier.
  4. Mark Yuying An & Roberto Ayala, 1996. "A Mixture Model of Willingness to Pay Distributions," Econometrics 9611002, EconWPA.
  5. Carson, Richard T & Wilks, Leanne & Imber, David, 1994. "Valuing the Preservation of Australia's Kakadu Conservation Zone," Oxford Economic Papers, Oxford University Press, vol. 46(0), pages 727-49, Supplemen.
  6. Richard Carson & Robert Mitchell & Michael Hanemann & Raymond Kopp & Stanley Presser & Paul Ruud, 2003. "Contingent Valuation and Lost Passive Use: Damages from the Exxon Valdez Oil Spill," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 25(3), pages 257-286, July.
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Citations

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Cited by:
  1. Nick Hanley & Bengt Kristrom, . "What’s it worth? Exploring value uncertainty using interval questions in Contingent Valuation," Working Papers 2002_10, Business School - Economics, University of Glasgow.
  2. An, Mark Yuying, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Working Papers 96-06, Duke University, Department of Economics.
  3. Riccardo Scarpa & Kenneth Willis & Guy Garrod, 2001. "Estimating Benefits for Effective Enforcement of Speed Reduction from Dichotomous-Choice CV," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 20(4), pages 281-304, December.
  4. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, EconWPA.
  5. Ramkishen S. Rejan, 1998. "The Currency And Financial Crisis In Southeast Asia - A Case Of `Sudden Deathã¢Â‚¬Â„¢ Or `Death Foretoldã¢Â‚¬Â„¢," Macroeconomics Working Papers 22381, East Asian Bureau of Economic Research.
  6. Ana Bedate & Luis Herrero & José Sanz, 2009. "Economic valuation of a contemporary art museum: correction of hypothetical bias using a certainty question," Journal of Cultural Economics, Springer, vol. 33(3), pages 185-199, August.
  7. Mark Yuying An & Roberto Ayala, 1996. "A Mixture Model of Willingness to Pay Distributions," Econometrics 9611002, EconWPA.

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