Accession Number : AD0278739

Title :   THE ROLE OF CONSTRAINTS IN THE THEORY OF LEAST SQUARES

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : ZELEN,M.

Report Date : MAY 1962

Pagination or Media Count : 1

Abstract : A unified account is presented of the theory of least squares and in particular describes the necessary modifications when linear restraints are imposed on the parameters. The developmen has be n gr atly influenced by the use of a 'generalized inverse' of a matrix which in turn leads to interesting new proofs of standard results and to some new results. The treatment distinguishes between restraints imposed for the purpos of obtaining unique solutions and real restraints. In the latter category, it is necessary to take into account whether the real restraints are estimable or non-estimable functions. Applications of the general theory are made to e case of equi-correlated variables (correlation unknown), the general case of a singular variance-covariance matrix among the observations, and to the case where linear restraints are subject to random error. (Author)

Descriptors :   MATRICES(MATHEMATICS), SAMPLING

Distribution Statement : APPROVED FOR PUBLIC RELEASE