No. 1117

Title:

A remark on projection estimator

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Density estimation, L_2 risk, orthonormal system

Abstract:

    We give a remark that the leading constant of the asymptotic bound for the $ L_2 $ risk of the projection estimator for a density on $ [-\pi,\pi] $ is $ 1/\pi $, not depending on the true density. In this sense, the projection estimator has a merit which the kernel estimators do not have.