ON CHEBYSHEV’S POLYNOMIALS OF NON-SMOOTH FUNCTIONAL AND ITS NONPARAMETRIC ESTIMATION
Abstract
In statistical inference, one of the basic problems is that of estimating functionals. This problem
is considered in the nonparametric set-up. The quality of estimation depends on smoothness
properties of the functional F. However, non smooth functionals lack some degree of properties
traditionally relied upon in estimation. This highlights the reason why standard techniques fail to
yield sharp results. In estimating non smooth functionals, the lower and upper bounds are
constructed for the MiniMax Risk. When working in the context of MiniMax estimation, the
lower bounds are important. A single- value MiniMax lower bound is established by applying
the general lower bound technique based on testing two composite hypotheses. A vital step is the
construction of two special priors and bounding the chi-square distance between two normal
mixtures. An estimator is constructed using approximation theory and Hermite polynomials and
is shown to be asymptotically sharp MiniMax when the means are bounded by a given value.
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.
