Finite Memory Estimation of Infinite Memory Processes

• Activity Number: 578
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zsolt Talata*+ and Imre Csiszar
• Companies: The University of Kansas and Hungarian Academy of Sciences
• Keywords: statistical estimation ; stationary ergodic processes ; infinite memory ; Markov approximation ; rate of convergence

Abstract

In many applications, random processes are assumed to have finite memory. This assumption, however, is not valid in practice in many cases. In this paper, stationary ergodic processes with finite alphabets are approximated by finite memory processes based on an n-length realization of the process. The d-distance is considered between the process and the estimated one. This is one of the most widely used metrics over stationary processes. Under the assumptions of summable continuity rate and non-nullness, a rate of convergence in d-distance is obtained, with explicit constants. Asymptotically, as n tends to infinity, the result is near the optimum.