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Consider the regression model 

<img src='content_image/297762.jpg'>

with a measurement of unobserved x ∗ given by ˜ z = x ∗ + ˜ u, with x $^{∗}$⊥ ˜ u conditionally on t . Assume that E (˜ u | t ) = 0 and that E ( v | x $^{∗}$, t ) = 0 . Then redefining all the densities and conditional expectations to be conditional on t we get the same system of convolution equations as in Table 2 for model 5 with the unknown functions now being conditional densities and the regression function, g. 

Conditioning requires assumptions that provide for existence of condi- tional distribution functions in S $^{∗}$. 

## 3 Solutions for the models. 

## 3.1 Existence of solutions 

To state results for nonparametric models it is important first to clearly indicate the classes of functions where the solution is sought. Assumption 1 requires that all the (generalized) functions considered are elements in the space of generalized functions S $^{∗}$. This implies that in the equations the operation of convolution applied to the two functions from S ∗ provides an element in the space S $^{∗}$. This subsection gives high level assumptions on the nonparametric classes of the unknown functions where the solutions can 

