Self-normalized Cramér type moderate deviations for martingales and applications (Q6632599)

The authors establish self-normalized Cramér type moderate deviations for martingales under some mild conditions. \N\NCramér's moderate deviations give a quantitative estimate for the relative error of the normal approximation and provide theoretical justifications for many estimators used in statistics.\N\NApplications of the result to Student's statistic, stationary martingale difference sequences and branching processes in a random environment are discussed.