Estimating features of a distribution from binomial data

We propose estimators of previous termfeatures of the distributionnext term of an unobserved random variable W. What is observed is previous termanext term sample of Y,V,X where previous termanext term binary Y equals one when W exceeds previous termanext term threshold V determined by experimental design, and X are covariates. Potential applications include bioassay and destructive duration analysis. Our empirical application is referendum contingent valuation in resource economics, where one is interested in previous termfeatures of the distributionnext term of values W (willingness to pay) placed by consumers on previous termanext term public good such as endangered species. Sample consumers with characteristics X are asked whether they favor (with Y=1 if yes and zero otherwise) previous termanext term referendum that would provide the good at previous termanext term cost V specified by experimental design. This paper provides estimators for quantiles and conditional on X moments of W under both nonparametric and semiparametric specifications.