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Asymptotic expansions for the CUSUM procedure in a change point problem. (English) Zbl 0848.60041

Summary: Let \(\{\xi_n\}\) be a sequence of i.i.d. random variables, \(N = \min \{n \geq 1 : \xi_1 + \cdots + \xi_n \notin [0,b)\}\). Asymptotic expansions at \(b\to\infty\) are obtained for the distribution and expectation of \(S_N\) under Cramér type conditions. These results are applied to the study of asymptotic properties of the CUSUM procedure in a change point problem.

MSC:

60F99 Limit theorems in probability theory
62E10 Characterization and structure theory of statistical distributions
60G50 Sums of independent random variables; random walks
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