Abstract
We use kernel-type estimators to estimate the time of change in the mean in a sequence of independent observations. Assuming that the size of the change is small two types of limit distributions are derived. The forms of the limit distributions depend on the behavior of the kernel at the end points. The argmax of a two-sided Brownian motion with polynomial drift is a possible limit, while the normal distribution is the limit when the kernel is zero at both boundaries.
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