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Inference on Parameters of a Shifted and Rescaled Wiener Process Based on Nonidentically Distributed Observations

The paper deals with inference about the parameters a and b 2 of the random process {bwt + at; t 0}, where {wt; t 0} is the Wiener process, a 0 and b 2 > 0. Inference is based on the first time when the process reaches a pre-specified positive boundary, where the boundary can be dierent for each observation. We focus on estimation and we shortly deal with testing hypotheses about one parameter at a time. We will show that neither the variance of estimators, nor the power of tests depend on the choice of the boundaries. These characteristics only depend on the number of observations and on the sum of the boundaries.