Conditional Boundary Crossing Probabilities with Applications to Change-Point Problems.
Abstract
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 P(S sdub n > mg(n/m) 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1986
- Accession Number
- ADA169606
Entities
People
- Barry James
- David Siegmund
- Kang L. James
Organizations
- Stanford University