Estimation for Linear Models with Unequal Variances.

Abstract

The problem considered is concerned with a linear model of the form y = Xbeta + e where y is an n-vector of observed variables X is a full rank n x m matrix of known numbers B is an m-vector of unknown parameters and e is an n-vector of unknown parameters and e is an n-vector of unknown 'residuals' whose independent elements e sub i satisfy E(e sub i) = 0 Var e sub i = (Sigma sub i)(Sup 2) (Unknown). A special case of particular importance arises when one makes the additional assumption of normal residuals e sub i = N(0, (Sigma(sub i)(Sup 2). The problem is to estimate the m-vector beta and the n-vector sigma sup 2 with elements (Sigma (Sub i)(Sup 2). In the special case when all (Sigma (Sub i)(Sup 2) are known to be equal the problem is that of classical linear model estimation. (Author)

Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1971
Accession Number
AD0734366

Entities

People

  • Herman Otto Hartley
  • K. S. E. Jayatillake

Organizations

  • Texas A&M University

Tags

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Linear Algebra
  • Regression Analysis.