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