On Inverse Estimation in Linear Regression

By M. Halperin. 1970

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Error asymmetry in causal and anticausal regression (2016, neutral): “However, this conclusion was criticized by many researchers (Berkson 1969; Halperin 1970; Parker et al. 2010) who argued that the conclusions made based on reverse regression do not reflect the actual relationship between cause and effect, which is obvious regarding (4).”
Forecast calibration and combination: A simple Bayesian approach for ENSO (2004, methodology): “An alternative criteria was proposed and the conditions of relative superiority of one method over the other were investigated in depth by Williams (1969), Berkson (1969), Halperin (1970), and Hoadley (1970) among others, and later on by Chow and Shao (1990).”
The Prediction Properties of Classical and Inverse Regression for the Simple Linear Calibration Problem (2010, background): “Berkson (1969) and Halperin (1970) present significant criticisms to Krutchkoff’s work.”
The Prediction Properties of Inverse and Reverse Regression for the Simple Linear Calibration Problem (2010, background): “Berkson (1969) and Halperin (1970) showed that for large samples, the reverse estimator has smaller mean squared error only when x lies within a small interval around x. Graybill (1976) and Seber (1977) developed a (1 − α)100% confidence region for an unknown value of x using the inverse regression…”