Self-consistent estimation of mean response functions and their derivatives

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Many methods have been developed for the nonparametric estimation of a mean response function, but most of these methods do not lend themselves to simultaneous estimation of the mean response function and its derivatives. Recovering derivatives is important for analyzing human growth data, studying physical systems described by differential equations, and characterizing nanoparticles from scattering data. In this article the authors propose a new compound estimator that synthesizes information from numerous pointwise estimators indexed by a discrete set. Unlike spline and kernel smooths, the compound estimator is infinitely differentiable; unlike local regression smooths, the compound estimator is self-consistent in that its derivatives estimate the derivatives of the mean response function. The authors show that the compound estimator and its derivatives can attain essentially optimal convergence rates in consistency. The authors also provide a filtration and extrapolation enhancement for finite samples, and the authors assess the empirical performance of the compound estimator and its derivatives via a simulation study and an application to real data.

Original languageEnglish
Pages (from-to)280-299
Number of pages20
JournalCanadian Journal of Statistics
Issue number2
StatePublished - Jun 2011


  • Compound estimator
  • Functional data analysis
  • Nonparametric regression
  • Self-consistency

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


Dive into the research topics of 'Self-consistent estimation of mean response functions and their derivatives'. Together they form a unique fingerprint.

Cite this