content_image/310767.jpg content_image/310768.jpg content_image/310769.jpg content_image/310772.jpg content_image/310773.jpg content_image/310774.jpg
that of − u by f$_{−}$$_{u}$. Then equation (4) gives 

<img src='content_image/310767.jpg'>

Additionally if expectation conditional on z exists, using independence be- tween z and u, 

then 

<img src='content_image/310768.jpg'>

<img src='content_image/310769.jpg'>

The system of equations (5 , 6) involves two unknown functions, f$_{u}$ and g, where usually the interest is in the regression function. 

The regression function could have instead of an observable argument, x, a mismeasured or latent argument, x $^{∗}$. The model could provide more equations if another measurement, x, on x ∗ were available. Consider 

<img src='content_image/310772.jpg'>

<img src='content_image/310773.jpg'>

<img src='content_image/310774.jpg'>

Here x, y, z are observed; assume that u is a Berkson type measurement er- ror independent of z with (unknown) density f, assume that u$_{y}$, u$_{x}$ have zero 

