Estimating the number of change points in a sequence of independent normal random variables

This work concerns the detection of the number of change points in a sequence of independent normal random variables. An estimator is proposed through some criterion, SC(k), of maximizing the log likelihood function with some penality term. The criterion is similar to that given by Yao (1988) only with a different penality term. An interesting result is that, under mild assumptions, the criterion SC(k) will be monotonically increasing in k [less-than-or-equals, slant] k0 but decreasing in k [greater-or-equal, slanted] k0 with probability approaching 1 as n --> [is proportional to]. Thus, weak consistency of the estimator based on the criterion can easily be obtained.