ON MINIMAX RISK OF NON-SMOOTH FUNCTIONAL, ITS ASYMPTOTIC PROPERTIES AND POLYNOMIAL ESTIMATION
Abstract
Nonparametric estimation of non-smooth functionals deals with highly structured
problems which arise, modeled or cast differently from the ones for which
mainline numerical methods have been designed. Non-smooth functional
estimation problems show some features that are different from those of estimating
smooth functionals. This is in terms of the optimal rates of convergence as well as
the technical tools needed for the analysis of the MiniMax lower bounds and the
construction of the optimal estimators. The main difficulty of estimating the nonsmooth functionals is traced back to the non differentiability of the absolute value
function at the origin. This is reflected both in the derivation of the lower bounds
and the construction of optimal estimators. The construction of the optimal
estimators of the non-smooth functionals is more complicated than those for linear
and quadratic functionals. In this study we consider asymptotic properties,
polynomial estimation and MiniMax risk involving non-smooth functionals.
Downloads
Author(s) and co-author(s) jointly and severally represent and warrant that the Article is original with the author(s) and does not infringe any copyright or violate any other right of any third parties, and that the Article has not been published elsewhere. Author(s) agree to the terms that the IJRDO Journal will have the full right to remove the published article on any misconduct found in the published article.
