Conditional Boundary Crossing Probabilities with Applications to Change-Point Problems.
STANFORD UNIV CA DEPT OF STATISTICS
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For normal random walks S sub 1, S sub 2, ..., formed from independent, identically distributed random variables X sub 1, X sub 2, ..., we determine the asymptotic behavior under regularity conditions of PS sdub n mgnm for some n m sub m mxi, m lambda0, xi g 1, where U sub m X sub one to the 2nd power ... X sub m to the 2nd power. The result is applied to a normal change-point problem to approximate null distributions of test statistics and to obtain approximate confidence sets for the change-point.
- Statistics and Probability