I encountered several times the following problem: Say I have a variable y dependent in a nonlinear way on m parameters ##\{x_i\}##, with ##i \in \{1,m\}##. However there is a linear relation between n>m functions ##f_j\in{x_i}##, i.e., ##y=\sum_j z_j f_j##. So I can get a solution of my problem determining first the coefficients ##f_j## by linear regression of y on ##z_j##, an then solving m of the n ##f_j## for the m ##x_i##.(adsbygoogle = window.adsbygoogle || []).push({});

Clearly, in the regression, I am not using some of the information about the correlation of the ##f_j## which I have in principle. Can the additional variance introduced by this procedure be estimated? Maybe you know about some paper on that topic?

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# A Nonlinear regression which can be partially reduced to linear regression

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