# Bahadur Efficiency of Tests for a Shift in Location of Normal Populations

• Jaap Praagman

## Summary

A sequence of independent random variables X 1,...,X N is said to have a change point n, if X 1,...,X N have a common distribution F and X n+1,..., X N have a common distribution G, GF. Consider the problem of testing the null hypothesis of no change, against the alternative of a one-sided change at an unknown change point n, when both F and G are normal with equal variance σ2. Most of the test statistics for this problem can be interpreted as generalizations of two-sample statistics (n known). In this chapter we derive the Bahadur efficiencies for two classes of statistics that are generalizations of the two-sample likelihood ratio statistics. The asymptotic results are compared with some small-sample power estimates based on Monte Carlo experiments.

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