SOME NUMERICAL RESULTS ON A COMPOUND DECISION PROBLEM
Abstract
When statistical decision problems of the same formal structure occur in large groups, rather than individually, there is often the possibility of reducing the total risk in the compound problem by using a decision procedure in which the decision in each individual problem is based not only on the random variable associated with that problem but also on the random variables associated with the other problems in the group. A very special case of the general procedure is presented so as to reduce to a minimum the mathematical apparatus required to obtain precise numerical results. The results obtained can be generalized in several directions. For example, two arbitrary simple hypotheses about the probability distribution of a random variable x may be tested. Moreover, the decision on the i(th) parameter value 0 sub i can be made to depend only on x(1), ..., x(1).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 11, 1961
- Accession Number
- AD0262426
Entities
People
- Herbert Robbins
Organizations
- Columbia University