On The Speed Of Convergence In The Central Limit Theorem Of Sequential Log-Likelihood Ratio Processes

Abstract

In this paper we,under a very general dependence set-up,obtaln a rate of convergence of the randomly stopped normallzed log-I lkel lhood ratlo statlstlc to standard normal varlables.Two examples are taken Into account.Non-unlform rates of convergence and bounds for Lp norms are also obtained under some qulte general condltlons.Martlngale techniques have been exploited throughout.

Keywords:

• Speed of convergence
• C. L. T
• randomly stopped log-Ilkellhood ratio process
• martlngale
• sequential estlmatlon