ESTIMATING THE NUMBER OF CHANGE-POINTS IN EXPONENTIAL-FAMILIES DISTRIBUTIONS

A simple method is proposed to detect the number of change points in a sequence of independent exponential family random variables. An estim ator to maximize some criterion, say SC(k), which is to maximize the l og-likelihood function with some penalty term, is used in detection. U nder some mild assumptions, the consistency of the estimator for the t rue number of change points and the boundedness between the estimated change locations and the true change location are obtained. Some simul ated results are given, and the Nile problem is investigated by this m ethod.