Estimating Durbin's approximation

Abstract

SUMMARY Some statistical procedures involve boundary crossing probabilities for processes that converge weakly to continuous Gaussian limits. When carrying out these procedures, boundary crossing probabilities associated with the limit processes may sometimes be substituted for the probabilities of interest. An approach to estimating Durbin's approximation to boundary crossing probabilities for continuous Gaussian processes is described here. When the covariance of the limit process satisfies a certain condition, the approach may be used to estimate the boundary crossing probabilities associated with the limit processes. Two examples illustrate the applicability of the approach, and the results of some simulation experiments are described.