Estimation of a Linear Transformation,
Abstract
A problem arising in the earth sciences can be formulated as follows: Pairs (X(i), y(i)) of independent p-dimensional normal random vectors having common covariance matrix Sigma squared are observed, i=1,2,...,n. It is assumed that x(i) and y(i) have respective mean vectors Xi(i) and B Xi(i), i=1,2,...,n, where the p x 1 vectors Xi(1), Xi(2),...,Xi(n), the p x p matrix B, and Sigma squared are unknown, and the p x p matrix sigma is assumed known. Maximum likelihood estimators of the unknown parameters are obtained when n or = 2p, and their behavior is studied both theoretically and in simulations. Some other approaches to the estimation of functional relationships are also studied, and are shown to yield the same estimators as maximum likelihood. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1972
- Accession Number
- AD0766316
Entities
People
- Geoffrey S. Watson
- Leon Jay Gleser
Organizations
- Johns Hopkins University