IDEAS home Printed from https://ideas.repec.org/p/duk/dukeec/96-02.html
   My bibliography  Save this paper

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

Author

Listed:
  • An, Mark Yuying
  • Ayala, Roberto A.

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.

Suggested Citation

  • An, Mark Yuying & Ayala, Roberto A., 1996. "Nonparametric Estimation of a Survivor Function with Across-Interval-Censored Data," Working Papers 96-02, Duke University, Department of Economics.
    • Handle: RePEc:duk:dukeec:96-02
    as

    Download full text from publisher

    File URL: http://www.econ.duke.edu/Papers/Abstracts96/abstract.96.02.html
    File Function: main text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, University Library of Munich, Germany.
    2. 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.
    3. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    4. 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.
    5. 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.
    6. Richard T. Carson, 2011. "Contingent Valuation," Books, Edward Elgar Publishing, number 2489.
    7. 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.
    8. 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).
    9. Daniel McFadden, 1994. "Contingent Valuation and Social Choice," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 76(4), pages 689-708.
    10. 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.
    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. An, Mark Yuying, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Working Papers 96-20, Duke University, Department of Economics.
    2. 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).
    3. 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.
    4. 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.
    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. 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.
    7. Mark Yuying An, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Econometrics 9611005, University Library of Munich, Germany.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.

    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. 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.
    4. 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.
    5. Ho-Young Kim & So-Yeon Park & Seung-Hoon Yoo, 2016. "Public Acceptability of Introducing a Biogas Mandate in Korea: A Contingent Valuation Study," Sustainability, MDPI, vol. 8(11), pages 1-16, October.
    6. 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.
    7. W. Michael Hanemann, 1994. "Valuing the Environment through Contingent Valuation," Journal of Economic Perspectives, American Economic Association, vol. 8(4), pages 19-43, Fall.
    8. 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.
    9. Lim, Seul-Ye & Kim, Hyo-Jin & Yoo, Seung-Hoon, 2017. "Public's willingness to pay a premium for bioethanol in Korea: A contingent valuation study," Energy Policy, Elsevier, vol. 101(C), pages 20-27.
    10. Ndebele, Tom & Forgie, Vicky, 2017. "Estimating the economic benefits of a wetland restoration programme in New Zealand: A contingent valuation approach," Economic Analysis and Policy, Elsevier, vol. 55(C), pages 75-89.
    11. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics.
    12. Rheinberger, Christoph M. & Schläpfer, Felix & Lobsiger, Michael, 2017. "A Novel Approach to Estimating the Demand Value of Road Safety," ETA: Economic Theory and Applications 254045, Fondazione Eni Enrico Mattei (FEEM).
    13. 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.
    14. Green, Donald & Jacowitz, Karen E. & Kahneman, Daniel & McFadden, Daniel, 1998. "Referendum contingent valuation, anchoring, and willingness to pay for public goods," Resource and Energy Economics, Elsevier, vol. 20(2), pages 85-116, June.
    15. 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.
    16. 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).
    17. Carlevaro, Fabrizio & Schlesser, C. & Binet , M. E. & Paul, M., 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.
    18. Haab, Timothy C. & McConnell, Kenneth E., 1997. "Referendum Models and Negative Willingness to Pay: Alternative Solutions," Journal of Environmental Economics and Management, Elsevier, vol. 32(2), pages 251-270, February.
    19. Henrik Andersson & James K. Hammitt & Kristian Sundström, 2015. "Willingness to Pay and QALYs: What Can We Learn about Valuing Foodborne Risk?," Journal of Agricultural Economics, Wiley Blackwell, vol. 66(3), pages 727-752, September.
    20. Gelo, Dambala & Koch, Steven F., 2015. "Contingent valuation of community forestry programs in Ethiopia: Controlling for preference anomalies in double-bounded CVM," Ecological Economics, Elsevier, vol. 114(C), pages 79-89.

    More about this item

    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
    • Q26 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Recreational Aspects of Natural Resources

    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:duk:dukeec:96-02. 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: Department of Economics Webmaster (email available below). General contact details of provider: http://econ.duke.edu/ .

    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.