Consider the following Model:
$Y_i = f(\theta, x_i) + e_i$
Where $\theta$ is the unknown d-dimesional parameter, and $e_i$ are some nice stochastic errors so maybe identical and normal distributed. $x_i$ are deterministic designpoints in $[0,1]$
Does someone know what optimal rate can be achieved for some parametric Estimator? So for example let $\theta_n$ denote the LSE, Then i am intrestet in
$E||\theta_n-\theta||^2\lesssim $ ???
with $||\theta_n-\theta||^2:=\sum_{k=1}^d |\theta_{n,i}-\theta_i|^2$