On Partitioning of a Sample with Binary-Type Questions in Lieu of Collecting Observations.
Abstract
The problem is to search for the t largest observations in a random sample of size n by asking binary type questions of the people (or items) in the sample without collecting any exact data whatever. The unordered and ordered cases are both considered; in the latter case the complete ranking is of special interest. Two different criteria of optimality are considered: (1) to minimize the expected number of questions required and (2) to maximize the probability of terminating the search in at most r questions for specified r. Optimal procedures are found and compared and in some sense the solutions for these two criteria are close to each other. The analysis is nonparametric in the sense that it holds for any underlying sampling distribution but the actual optimal procedures depend on the specified distribution. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1979
- Accession Number
- ADA081523
Entities
People
- Kenneth J. Arrow
- Leon Pesotchinsky
- Milton Sobel
Organizations
- Stanford University