A critical review of univariate non-parametric estimation of first derivatives.
- Resource Type
- Article
- Authors
- Bernstein, David H.
- Source
- Journal of Statistical Computation & Simulation. Nov2022, Vol. 92 Issue 16, p3511-3528. 18p.
- Subject
- *NONPARAMETRIC estimation
*MONTE Carlo method
*AKAIKE information criterion
*STATISTICAL smoothing
*UNIVARIATE analysis
- Language
- ISSN
- 0094-9655
This paper gives new guidance for selection of univariate non-parametric derivative estimators with non-iid errors in finite samples. It is shown via an extensive set of Monte Carlo simulations that the generalized C P criterion of Charnigo et al. (A generalized C P criterion for derivative estimation. Technometrics. 2011;53:238–253.) with spline smoothing performs the best in situations with minimal noise. For increased noise, generalized cross-validation of Craven and Wahba (Smoothing noisy data with spline functions. Numer Math. 1978;31:377–403) with P spline smoothing and the improved Akaike Information Criterion of Hurvich et al. (Smoothing parameter selection in nonparametric regression using an improved Akaike information criterion. J R Stat Soc Ser B. 1998;60:271–293.) with P spline smoothing are preferred. In the class of kernel smoothing and local regression methods, the local-cubic estimator of Henderson et al. (Gradient-based smoothing parameter selection for nonparametric regression estimation. J Econom. 2015;184:233–241.) generally outperforms its competitors. An internal meta-analysis separately favours the generalized C P method and P spline smoothing. The empirical example given provides support for use of the local-cubic estimator. [ABSTRACT FROM AUTHOR]