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Linear regression by functional least squares

Published online by Cambridge University Press:  14 July 2016

C. R. Heathcote
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Abstract

The standard linear regression model is analysed using a method called functional least squares which yields a family of estimators for the slope parameter indexed by a real variable t, |t| ≦ T. The choice t = 0 corresponds to ordinary least squares, non-zero values being appropriate if the error distribution is long-tailed, and it is argued that the approach is a natural extension of least squares methodology. It emerges that the asymptotic normal distribution of these estimators has a covariance matrix characterised by a scalar function of t, called the variance function, which is determined by the error distribution. Properties of this variance function suggest graphical criteria for detecting departures from normality.

Keywords

REGRESSIONROBUST ESTIMATIONOUTLIERS
Type
Part 5 — Statistical Theory
Information
Journal of Applied Probability , Volume 19 , Issue A , 1982 , pp. 225 - 239
Copyright
Copyright © 1982 Applied Probability Trust 

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