## Derivative Estimation Based on Difference Sequence via Locally Weighted Least Squares Regression

*WenWu Wang, Lu Lin*; 16(Dec):2617−2641, 2015.

### Abstract

A new method is proposed for estimating derivatives of a
nonparametric regression function. By applying Taylor expansion
technique to a derived symmetric difference sequence, we obtain
a sequence of approximate linear regression representation in
which the derivative is just the intercept term. Using locally
weighted least squares, we estimate the derivative in the linear
regression model. The estimator has less bias in both valleys
and peaks of the true derivative function. For the special case
of a domain with equispaced design points, the asymptotic bias
and variance are derived; consistency and asymptotic normality
are established. In simulations our estimators have less bias
and mean square error than its main competitors, especially
second order derivative estimator.

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