I am interested in applications (to data) of non-parametric statistics, and my question concerned the Gaussian white noise model defined by, $$ X_{t_1, \ldots, t_d}=f\left(t_1, \ldots, t_d\right) d t_1 \ldots d t_d+\theta d W_{t_1, \ldots, t_d} $$ with $W$ a $d$-parameters Wiener field, $f$ a bounded function over $[0,1]^d$ and $\theta \geq 0$ the level of noise.
It seems to be a classical model in non-parametric statistics. Introduced by Ibragimov and Has'minskii in the 70's it has been since often considered as a theoretical unifying framework because of its equivalence properties with other model and its ease of study.
But, i wonder in what kind of practical context this model can be relevant ? Applied papers I have come across mostly consider a density model or a non-parametric regression model and I struggle to find a paper considering Gaussian White Noise Model for application to data. Is there any work in this direction ?
