content_image/307448.jpg content_image/307447.jpg content_image/307449.jpg content_image/307451.jpg content_image/307450.jpg content_image/307446.jpg
## 1 Introduction 

Consider i.i.d. observations ( x$_{i}$ , y$_{i}$ ) , i = 1 , ..., n, given by the nonlinear model with random predictors: 

where x$_{i}$ ∈ R q and e$_{i}$ are independent, and the unknown parameter vector θ$_{0}$ ranges in a set Θ ⊂ R $^{p}$. An important case, usually called separable , are models where p = p$_{1}$ + p$_{2}$ and θ$_{0}$ = ( α$_{0}$, β$_{0}$ ) with α$_{0}$ ∈ A ⊂ R p 1 and β$_{0}$ ∈ B ⊂ R p 2 , and g of the form p 2 

where h$_{j}$ ( j = 1 , ..., p$_{2}$ ) are functions of X × R p 2 → R. Usually B is the whole of R p 2 or an unbounded subset of it. Examples are the Michaelis-Menten model, with 

the logistic growth model, with 

<img src='content_image/307448.jpg'>

the exponential decay model, with 

<img src='content_image/307447.jpg'>

and the exponential growth model, like (5) but with α$_{j}$ > 0 . 

The classical least squares estimate (LSE) is given by 

<img src='content_image/307449.jpg'>

<img src='content_image/307451.jpg'>

<img src='content_image/307450.jpg'>

<img src='content_image/307446.jpg'>

