Abstract
Estimation of a function, or its derivatives via nonparametric regression requires selection of one or more tuning parameters. In the present work, we propose a tuning parameter selection criterion called DCp for nonparametric derivative estimation in random design. Our criterion is general in that it can be applied with any nonparametric estimation method which is linear in the observed outcomes. Charnigo et al. [A generalized (Formula presented.) criterion for derivative estimation. Technometrics. 2011;53(3):238–253] had proposed a GCp criterion for a similar purpose, assuming values of the covariate to be fixed and constant error variance. Here we consider the setting with random design and non-constant error variance since the covariate values will not generally be fixed and equally spaced in real data applications. We justify DCp in this setting both theoretically and by simulation. We also illustrate use of DCp with two economics data sets.
| Original language | English |
|---|---|
| Pages (from-to) | 1402-1425 |
| Number of pages | 24 |
| Journal | Statistics |
| Volume | 57 |
| Issue number | 6 |
| DOIs | |
| State | Published - 2023 |
Bibliographical note
Publisher Copyright:© 2023 Informa UK Limited, trading as Taylor & Francis Group.
Funding
Sisheng Liu's research is supported by the Scientific Research Fund of Hunan Provincial Education Department [grant number 22B0037]. We gratefully acknowledge the coding work from Charnigo et al. [3] since some of R code for our simulation study was adapted from their work. We thank the associate editor and two anonymous peer reviewers for constructive suggestions.
| Funders | Funder number |
|---|---|
| Scientific Research Foundation of Hunan Provincial Education Department | 22B0037 |
Keywords
- Nonparametric derivative estimation
- empirical derivative
- heteroskedasticity
- random covariate
- tuning parameter selection
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty