A nonlinear parking problem
Keener, Robert; Rudolf Lerche, Hans; Woodroofe, Michael; Keener, Robert; University of Michigan; Rudolf Lerche, Hans; University of Freiburg; Woodroofe, Michael; University of Michigan
Журнал:
Sequential Analysis
Дата:
1995
Аннотация:
The problem of minimizing Eg<sub>c</sub>(Z<sub>t</sub>) is considered asymptotically, where Z<sub>0</sub>,Z<sub>1</sub>,… is a perturbed random walk and g<sub>c</sub> are convex functions which are minimized at values that approach ∞ as c ↓ 0. It is shown that a first passage time is asymptotically optimal, and the boundary for this time is characterized in terms of g<sub>c</sub> and the limiting distribution of the excess over the boundary. Applications to change point problems and power one tests are presented.
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