# Accession Number:

## AD0766316

# Title:

## Estimation of a Linear Transformation,

# Descriptive Note:

# Corporate Author:

## JOHNS HOPKINS UNIV BALTIMORE MD DEPT OF STATISTICS

# Personal Author(s):

# Report Date:

## 1972-08-01

# Pagination or Media Count:

## 19.0

# Abstract:

A problem arising in the earth sciences can be formulated as follows Pairs Xi, yi of independent p-dimensional normal random vectors having common covariance matrix Sigma squared are observed, i1,2,...,n. It is assumed that xi and yi have respective mean vectors Xii and B Xii, i1,2,...,n, where the p x 1 vectors Xi1, Xi2,...,Xin, 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

# Descriptors:

# Subject Categories:

- Geology, Geochemistry and Mineralogy
- Statistics and Probability