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

  • Mark Yuying An

    (Duke Uniersity)

  • Roberto Ayala

    (Central Bank, Ecuador)

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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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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  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. 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.
  3. Mark Yuying An & Roberto Ayala, 1996. "A Mixture Model of Willingness to Pay Distributions," Econometrics 9611002, EconWPA.
  4. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
  5. 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.
  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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