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

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Author Info
An, Mark Yuying
Ayala, Roberto A.

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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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Paper provided by Duke University, Department of Economics in its series Working Papers with number 96-02.

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Date of creation: 1996
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Handle: RePEc:duk:dukeec:96-02

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Find related papers by JEL classification:
C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models
Q26 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Renewable Resources and Conservation - - - Recreational Aspects of Natural Resources

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  1. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, EconWPA. [Downloadable!]
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  2. An, Mark Y. & Roberto Ayala, 1995. "A Mixture Model of Willingness to Pay Distributions," Working Papers 95-21, Duke University, Department of Economics. [Downloadable!]
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(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. Mark Yuying An & Roberto Ayala, 1996. "A Mixture Model of Willingness to Pay Distributions," Econometrics 9611002, EconWPA. [Downloadable!]
    Other versions:
  2. Mark Yuying An, 1996. "Semiparametric Estimation of Willingness to Pay Distributions," Econometrics 9611001, EconWPA. [Downloadable!]
    Other versions:
  3. Mark Yuying An, 1996. "Statistical Inference of a Bivariate Proportional Hazard Model with Grouped Data," Econometrics 9611005, EconWPA. [Downloadable!]
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. Nick Hanley & Bengt Kristrom, . "What’s it worth? Exploring value uncertainty using interval questions in Contingent Valuation," Working Papers 2002_10, Department of Economics, University of Glasgow. [Downloadable!]
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