Biological processes are commonly described Ordinary Differential Equation (ODE) taking a
general form, :
$$ ̇
X'=f(X,t,\theta)
$$

as it gives the ability to have a mechanistic descripion of biological systems. These ODE critically
rely on a set of parameter θ which have to be estimated from sparse and noisy data. Classical
statistical estimators (such as least squares, maximum likelihood) often fail to give proper estimation
due to the implicit nature of the model, heavy computation and the presence of local minima in
the objective function. New methods have been proposed to circumvent these difficulties. Among
them, two step estimators use classical nonparametric technics in order to “regularize” the estimation
problem. These estimators use:
1. A first preliminary smoothing step to obtain an estimator of the solution $\varphi^∗$ (called $\hat{X_n}$ )
directly from the data,
2. A second step of parametric estimation by optimizing a functional criteria constructed from
$\hat{X_n}$ .
Our aim here will be to describe these methods theoritically and through a simple example coming
from biological modeling.