  We study the nonparametric change point estimation for common changes in the
means of panel data. The consistency of estimates is investigated when the
number of panels tends to infinity but the sample size remains finite. Our
focus is on weighted denoising estimates, involving the group fused LASSO, and
on the weighted CUSUM estimates. Due to the fixed sample size, the common
weighting schemes do not guarantee consistency under (serial) dependence and
most typical weightings do not even provide consistency in the i.i.d. setting
when the noise is too dominant. Hence, on the one hand, we propose a consistent
covariance-based extension of existing weighting schemes and discuss
straightforward estimates of those weighting schemes. The performance will be
demonstrated empirically in a simulation study. On the other hand, we derive
sharp bounds on the change to noise ratio that ensure consistency in the i.i.d.
setting for classical weightings.
