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Least-Squares Theory Based on General Distributional Assumptions with an Application to the Incomplete Observations Problem

Published online by Cambridge University Press:  01 January 2025

B. M. S. Van Praag ,
T. K. Dijkstra  and
J. Van Velzen
B. M. S. Van Praag*
Affiliation:
Econometric Institute, Erasmus University, Rotterdam
T. K. Dijkstra
Affiliation:
University of Groningen
J. Van Velzen
Affiliation:
IBM, The Netherlands
*
Requests for reprints should be sent to B. M. S. Van Praag, Erasmus University, Econometric Institute, P.O. Box 1738, 3000 DR Rotterdam, THE NETHERLANDS.
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Abstract

The linear regression model y=β′x+ ε is reanalyzed. Taking the modest position that β′x is an approximation of the “best” predictor of y we derive the asymptotic distribution of b and R2, under mild assumptions.

The method of derivation yields an easy answer to the estimation of β from a data set which contains incomplete observations, where the incompleteness is random.

Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 1 , March 1985 , pp. 25 - 36
Copyright
Copyright © 1985 The Psychometric Society

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