content_image/317363.jpg content_image/317360.jpg content_image/317361.jpg content_image/317362.jpg
## 7 Limit properties of kernel estimators of con- ditional mean function. 

Suppose that with d$_{y}$ = 1 the conditional mean function m ( x ) = E$_{y}$$_{|}$$_{x}$y exists; by (21) it then can be represented as 

<img src='content_image/317363.jpg'>

Consider the usual kernel estimator 

that can also be represented as 

Then for any continuously differentiable ˜ ψ ( x ) 

<img src='content_image/317360.jpg'>

<img src='content_image/317361.jpg'>

<img src='content_image/317362.jpg'>

