Smoothed Nonparametric Derivative Estimation Based on Weighted Difference Sequences

We present a simple but effective fully automated framework for estimating derivatives nonparametrically based on weighted difference sequences. Although regression estimation is often studied more, derivative estimation is of equal importance. For example in the study of exploration of structures in curves, comparison of regression curves, analysis of human growth data, etc. Via the introduced weighted difference sequence, we approximate the true derivative and create a new data set which can be smoothed by any nonparametric regression estimator. However, the new data sets created by this technique are no longer independent and identically distributed (i.i.d.) random variables. Due to the non-i.i.d. nature of the data, model selection methods tend to produce bandwidths (or smoothing parameters) which are too small. In this paper, we propose a method based on bimodal kernels to cope with the non-i.i.d. data in the local polynomial regression framework.