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In a 1989 paper on orthogonal regression, Ammann and Van Ness write:

An important caveat should be noted. The errors-variables-model is useful when the primary goal is to estimate the model parameters rather than prediction. If the EV model holds with certain mild symmetry conditions on the (not necessarily Gaussian) error distributions; then, if you wish to predict Y given x, ordinary regression of y on x should be used (see Cheng and Van Ness (1987))

Unfortunately, the cited paper is difficult to find (or unpublished?).

Can someone explain this statement?

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  • $\begingroup$ It's a published paper, as the citation bears out. $\endgroup$ – Nick Cox Nov 11 '19 at 7:29
  • $\begingroup$ @Nick Cox it references a “submitted” technical report. Can you find it? $\endgroup$ – rhombidodecahedron Nov 11 '19 at 8:08
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    $\begingroup$ I see what you mean: you’re referring to the 1987 reference. I don’t have access to this 1989 paper beyond the abstract. But there’s a book by the same authors, is there not? $\endgroup$ – Nick Cox Nov 11 '19 at 8:10
  • $\begingroup$ In my answer, I provide the link for the (published version of the) paper provided, plus a short quote showing this is what you are interested in. $\endgroup$ – Alex. C-L - Reinstate Monica Nov 25 '19 at 20:28
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The published version of the Cheng and Van Ness paper that you are interested in can be found here:

CHENG, CHILUN et VAN NESS, JOHN W. Errors-in-Variables Regression. In : Statistical Analysis of Measurement Error Models and Applications: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference Held June 10-16, 1989, with Support from the National Science Foundation and the US Army Research Office. American Mathematical Soc., 1990. p. 227. *

They state in page 2: "Note that if the primary purpose of the modeling is to predict the unobserved y form the unobserved X, then orthogonal regression might not prove useful. (See the Appendix and, for example, the discussion in Fuller (1987), Section 1.6.3.)"

And you are interested by the Appendix: "Prediction for Errors-in-Variables Data", that shows through much computations that: "Under general conditions, ordinary regressions will provide at least as good prediction models as orthgonal regressions for the errors-in-variables model."

link:* https://books.google.de/books?hl=en&lr=&id=TRkcCAAAQBAJ&oi=fnd&pg=PA227&dq=info:E750hOTH1gkJ:scholar.google.com&ots=_wmkpmgNSQ&sig=P067RjjogXJMOJa2k_dd4ImngaM&redir_esc=y#v=onepage&q&f=false

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