The objective of the present paper is to develop a minimax theory for the varying coefficient
model in a non-asymptotic setting. We consider a high-dimensional sparse varying
coefficient model where only few of the covariates are present and only some of those covariates
are time dependent. Our analysis allows the time dependent covariates to have different
degrees of smoothness and to be spatially inhomogeneous. We develop the minimax lower
bounds for the quadratic risk and construct an adaptive estimator which attains those lower
bounds within a constant (if all time-dependent covariates are spatially homogeneous) or
logarithmic factor of the number of observations.
KLOPP, O. et PENSKY, M. (2015). Sparse high-dimensional varying coefficient model : non-asymptotic minimax study. Annals of Statistics, 43(3), pp. 1273-1299.