Comparison study on smoothing parameter and sample size in nonparametric fuzzy local polynomial regression models

In this paper, we considered the relationship between the smoothing parameter value and sample size as a simulation study in nonparametric fuzzy local polynomial regression. For this aim, we developed fuzzy version of generalized cross-validation criteria (GCV) for selecting smoothing parameter in nonparametric fuzzy local polynomial models. Besides the local linear models, local cubic models are also used in these simulations. The appropriate smoothing parameters are selected by GCV criteria for different sample size and then performances of the models are compared using these appropriate smoothing parameters with sample sizes.