content_image/303851.jpg content_image/303852.jpg content_image/303853.jpg content_image/303854.jpg
space), 

<img src='content_image/303851.jpg'>

Therefore a system of convolution equations arises for the unknown function g and functions h$_{k}$, where h$_{k}$ ( x ) = x$_{k}$g ( x ) , 

<img src='content_image/303852.jpg'>

Another model that leads to a system of equations is nonparametric re- gression with Berkson error (see, e.g. Meister, 2009 for review). Consider a nonparametric regression model 

<img src='content_image/303853.jpg'>

where x may be correlated with the error, u$_{y}$, but where some instruments, z, are available such that 

<img src='content_image/303854.jpg'>

with z is independent of u (Berkson error) and E ( u$_{y}$ | z ) = 0 . Denote the density of x by f$_{x}$, density of z by f$_{z}$, density of u by f u and correspondingly 

