This paper considers transformations of nonlinear semiparametric mean functions that yield moment conditions for estimation. Such transformations are said to be information equivalent if they yield the same asymptotic efficiency bound. I derive a unified theory of algebraic equivalence for...

Some properties of following two groups of equations are developed in this article: 1) x^2+y^2+z^2+v^2=dXYZ, x^i+y^i+z^i +v^i= dXYZ (where i is an integer), x^2+y^2+z^2= gXYZ and x^2+y^2+z^2+v^2+u^2=dXYZ, x^3+y^3+z^3=dXYZ, and x^6+y^6+z^6=dXYZ, x^3+y^3+z^3+x^6+y^6+z^6=dXYZ,...