ESTIMATING DURBIN APPROXIMATION

Some statistical procedures involve boundary crossing probabilities fo r processes that converge weakly to continuous Gaussian limits. When c arrying out these procedures, boundary crossing probabilities associat ed with the limit processes may sometimes be substituted for the proba bilities 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 examp les illustrate the applicability of the approach, and the results of s ome simulation experiments are described.