The Population-Sample Decomposition Method

A Distribution-Free Estimation Technique for Minimum Distance Parameters

I. Introduction to the Population-Sample Decomposition Approach.
I.1 The linear statistical model.
I.2 Minimum distance parameters subject to minimal model assumptions.
II. The Estimation of Linear Relations; The Sample Part of PSD.
II.1 Method of moments and asymptotic distribution theory.
II.2 Asymptotic estimation of covariance functions.
III. Principal Relations.
III.1 Basic formulation of the principal relations.
III.2 The distance matrix Q.
III.3 Simultaneous equations systems.
III.4 Seemingly unrelated regressions.
III.5 Restricted seemingly unrelated regressions.
III.6 Canonical correlation analysis.
IV. Principal Factors.
IV.1 Basic formulation of principal factors.
IV.2 Principal relations versus principal factors.
IV. 3 Principal components analysis.
V. Goodness-of-Fit Measures.
V. 1 Coefficients of multiple correlation and angles between random vectors.
V.2 Coefficients of linear association for principal relations and principal factors.
V.3 Coefficients of linear association for simultaneous equations systems.
V.4 Coefficients of linear association for seemingly unrelated regressions.
VI. Review.
VI.1 A schematic representation of the parameters.
VI.2 List of notation and summary of results.
VII. Computational Aspects of the Population-Sample Decomposition.
VII.1 Fourth-order central moments.
VII.2 Pre- and post-multiplication of V by the gradient matrix.
VII.3 The PSD method in practice.
Preliminaries on matrix algebra.
References.
Author Index.