A changepoint statistic with uniform type I error probabilities

ABSTRACT

Likelihood ratio tests for a change in mean in a sequence of independent, normal random variables are based on the maximum two-sample t-statistic, where the maximum is taken over all possible changepoints. The maximum t-statistic has the undesirable characteristic that Type I errors are not uniformly distributed across possible changepoints. False positives occur more frequently near the ends of the sequence and occur less frequently near the middle of the sequence. In this paper we describe an alternative statistic that is based upon a minimum p-value, where the minimum is taken over all possible changepoints. The p-value at any particular changepoint is based upon both the two-sample t-statistic at that changepoint and the probability that the maximum two-sample t-statistic is achieved at that changepoint. The new statistic has a more uniform distribution of Type I errors across potential changepoints and it compares favorably with respect to statistical power, false discovery rates, and the mean square error of changepoint estimates.