On the estimation of the derivatives of a function with the derivatives of an estimate
Journal
Journal of Multivariate Analysis
Date Issued
January 1989
Author(s)
DOI
10.1016/0047-259X(89)90102-4
Abstract
Let θ̂n(x) be an estimator of a smooth function θ(x). It is proved that θ(x) can be estimated easier than its derivative θ(s)(x), providing for |θ̂n (s) - θ(s)|q an upper bound that depends on |θ̂n - θ|q. The same bound can be used as a tool to derive automatically rates of convergence when we are estimating derivatives of densities or regression functions.
Subjects