  We look into the nonparametric regression estimation with additive and
multiplicative noise and construct adaptive thresholding estimators based on
Laguerre series. The proposed approach achieves asymptotically near-optimal
convergence rates when the unknown function belongs to Laguerre-Sobolev space.
We consider the problem under two noise structures; (1) { i.i.d.} Gaussian
errors and (2) long-memory Gaussian errors. In the { i.i.d.} case, our
convergence rates are similar to those found in the literature. In the
long-memory case, the convergence rates depend on the long-memory parameters
only when long-memory is strong enough in either noise source, otherwise, the
rates are identical to those under { i.i.d.} noise.
