IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/9611003.html

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

Author

Listed:
  • 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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Mark Yuying An & Roberto Ayala, 1996. "Nonparametric Estimation of a Survivor Function with Across- Interval-Censored Data," Econometrics 9611003, University Library of Munich, Germany.
    • 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.
    as

    Download full text from publisher

    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9611/9611003.pdf
    Download Restriction: no
    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/em/papers/9611/9611003.ps.gz
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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, Springer;European Association of Environmental and Resource Economists, vol. 25(3), pages 257-286, July.
    2. W. Michael Hanemann, 1984. "Welfare Evaluations in Contingent Valuation Experiments with Discrete Responses," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 66(3), pages 332-341.
    3. Daniel McFadden, 1994. "Contingent Valuation and Social Choice," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(4), pages 689-708.
    4. Michael Hanemann & John Loomis & Barbara Kanninen, 1991. "Statistical Efficiency of Double-Bounded Dichotomous Choice Contingent Valuation," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 73(4), pages 1255-1263.
    5. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
    6. Richard T. Carson, 2011. "Contingent Valuation," Books, Edward Elgar Publishing, number 2489.
    7. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    8. 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 727-749, Supplemen.
    9. 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 269-276, May.
    10. Bishop, Richard C. & Heberlein, Thomas A., 1979. "Measuring Values Of Extramarket Goods: Are Indirect Measures Biased?," 1979 Annual Meeting, July 29-August 1, Pullman, Washington 277818, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    11. Richard C. Bishop & Thomas A. Heberlein, 1979. "Measuring Values of Extramarket Goods: Are Indirect Measures Biased?," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 61(5), pages 926-930.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Czajkowski, Mikołaj & Zawojska, Ewa & Meade, Norman & da Motta, Ronaldo Seroa & Welsh, Mike & Ortiz, Ramon Arigoni, 2024. "On the inference about a willingness-to-pay distribution using contingent valuation data," Ecological Economics, Elsevier, vol. 222(C).
    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. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
    4. 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;The Association for Cultural Economics International, vol. 33(3), pages 185-199, August.
    5. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    6. Jeongyong Kim & Karen Bandeen-Roche, 2019. "Parametric estimation of association in bivariate failure-time data subject to competing risks: sensitivity to underlying assumptions," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(2), pages 259-279, April.
    7. José Sanz & Luis Herrero & Ana Bedate, 2003. "Contingent Valuation and Semiparametric Methods: A Case Study of the National Museum of Sculpture in Valladolid, Spain," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 27(3), pages 241-257, November.
    8. W. George Hutchinson & Riccardo Scarpa & Susan M. Chilton & T. McCallion, 2001. "Parametric and Non‐Parametric Estimates of Willingness to Pay for Forest Recreation in Northern Ireland: A Discrete Choice Contingent Valuation Study with Follow‐Ups," Journal of Agricultural Economics, Wiley Blackwell, vol. 52(1), pages 104-122, January.
    9. Brett Day, 2007. "Distribution-free estimation with interval-censored contingent valuation data: troubles with Turnbull?," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 37(4), pages 777-795, August.
    10. Hongsheng Dai & Marialuisa Restaino & Huan Wang, 2016. "A class of nonparametric bivariate survival function estimators for randomly censored and truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 736-751, October.
    11. Riccardo Scarpa & Kenneth Willis & Guy Garrod, 2001. "Estimating Benefits for Effective Enforcement of Speed Reduction from Dichotomous-Choice CV," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 20(4), pages 281-304, December.
    12. Nick Hanley & Bengt Kristrom, "undated". "What’s it worth? Exploring value uncertainty using interval questions in Contingent Valuation," Working Papers 2002_10, Business School - Economics, University of Glasgow.
    13. Carla Moreira & Jacobo de Uña-Álvarez, 2010. "Bootstrapping the NPMLE for doubly truncated data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 567-583.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Richard T. Carson & Miko_aj Czajkowski, 2014. "The discrete choice experiment approach to environmental contingent valuation," Chapters, in: Stephane Hess & Andrew Daly (ed.), Handbook of Choice Modelling, chapter 9, pages 202-235, Edward Elgar Publishing.
    2. Vivien Foster & Susana Mourato, 2003. "Elicitation Format and Sensitivity to Scope," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 24(2), pages 141-160, February.
    3. Hanemann, W. Michael & Kanninen, Barbara, 1996. "The Statistical Analysis Of Discrete-Response Cv Data," CUDARE Working Papers 25022, University of California, Berkeley, Department of Agricultural and Resource Economics.
    4. Robert J. Johnston & Kevin J. Boyle & Wiktor (Vic) Adamowicz & Jeff Bennett & Roy Brouwer & Trudy Ann Cameron & W. Michael Hanemann & Nick Hanley & Mandy Ryan & Riccardo Scarpa & Roger Tourangeau & Ch, 2017. "Contemporary Guidance for Stated Preference Studies," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 4(2), pages 319-405.
    5. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    6. W. George Hutchinson & Riccardo Scarpa & Susan M. Chilton & T. McCallion, 2001. "Parametric and Non‐Parametric Estimates of Willingness to Pay for Forest Recreation in Northern Ireland: A Discrete Choice Contingent Valuation Study with Follow‐Ups," Journal of Agricultural Economics, Wiley Blackwell, vol. 52(1), pages 104-122, January.
    7. Choi, Jihye & Kim, Justine Jihyun & Lee, Jongsu, 2024. "Public willingness to pay for mitigating local conflicts over the construction of renewable energy facilities: A contingent valuation study in South Korea," Energy Policy, Elsevier, vol. 185(C).
    8. Fabrizio Carlevaro & C. Schlesser & M. E. Binet & M. Paul, 2007. "Econometric Modeling and Analysis of Residential Water Demand Based on Unbalanced Panel Data," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 8(4), pages 81-102.
    9. Richard Bennett & Douglas Larson, 1996. "Contingent Valuation Of The Perceived Benefits Of Farm Animal Welfare Legislation: An Exploratory Survey," Journal of Agricultural Economics, Wiley Blackwell, vol. 47(1‐4), pages 224-235, January.
    10. Cho, Seong-Hoon & Yen, Steven T. & Bowker, J.M. & Newman, David H., 2008. "Modeling Willingness to Pay for Land Conservation Easements: Treatment of Zero and Protest Bids and Application and Policy Implications," Journal of Agricultural and Applied Economics, Cambridge University Press, vol. 40(1), pages 267-285, April.
    11. Giffoni, Francesco & Florio, Massimo, 2023. "Public support of science: A contingent valuation study of citizens' attitudes about CERN with and without information about implicit taxes," Research Policy, Elsevier, vol. 52(1).
    12. Massimo Florio & Francesco Giffoni, 2020. "A contingent valuation experiment about future particle accelerators at CERN," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-24, March.
    13. Talwar, Shagorika, 1995. "An evaluation of statistical efficiency and bias trade-off involved with the use of follow-up questioning in the contingent valuation of environmental amenities," ISU General Staff Papers 1995010108000018160, Iowa State University, Department of Economics.
    14. Richard O‘Conor & Magnus Johannesson & Per-Olov Johansson, 1999. "Stated Preferences, Real Behaviour and Anchoring: Some Empirical Evidence," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 13(2), pages 235-248, March.
    15. Brett Day & Jose Luis Pinto Prades, 2008. "Sequencing Anomalies in Choice Experiments," Working Papers 08.10, Universidad Pablo de Olavide, Department of Economics.
    16. John C. Whitehead & Tim Haas & Lynne Lewis & Leslie Richardson & Pete Schuhmann, 2025. "A Meta-Analysis of SBC Contingent Valuation: Willingness to Pay Estimates, Determinants of Reliability and Replication of Split-Sample Hypothesis Tests," Working Papers 25-11, Department of Economics, Appalachian State University.
    17. W. Michael Hanemann, 1994. "Valuing the Environment through Contingent Valuation," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 19-43, Fall.
    18. Abay Asfaw & Joachim Braun, 2005. "Innovations in Health Care Financing: New Evidence on the Prospect of Community Health Insurance Schemes in the Rural Areas of Ethiopia," International Journal of Health Economics and Management, Springer, vol. 5(3), pages 241-253, September.
    19. Hermann Donfouet & P. Jeanty & P.-A. Mahieu, 2014. "Dealing with internal inconsistency in double-bounded dichotomous choice: an application to community-based health insurance," Empirical Economics, Springer, vol. 46(1), pages 317-328, February.
    20. Lee, Chul-Yong & Heo, Hyejin, 2016. "Estimating willingness to pay for renewable energy in South Korea using the contingent valuation method," Energy Policy, Elsevier, vol. 94(C), pages 150-156.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • Q20 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpem:9611003. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: EconWPA The email address of this maintainer does not seem to be valid anymore. Please ask EconWPA to update the entry or send us the correct address (email available below). General contact details of provider: https://econwpa.ub.uni-muenchen.de .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.