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

Estimation in nonparametric regression model with additive and multiplicative noise via Laguerre series