Kybernetika 31 no. 3, 221-237, 1995

The role of Hájek's convolution theorem in statistical theory

Rudolf Beran


Hájek's [17] convolution theorem was a major advance in understanding the classical information inequality. This re-examination of the convolution theorem discusses historical background to asymptotic estimation theory; the role of superefficiency in current estimation practice; the link between convergence of bootstrap distributions and convolution structure; and a dimensional asymptotics view of superefficiency.


62B10, 62F12