Name of robustness check where you exclude individuals? I have a panel dataset and to check the robustness of the results, I'm re-estimating the models with each panel unit excluded once. Does this robustness check habe a particular name?
Depending on the context this is sometimes called Jackknife resampling


  In statistics, the jackknife is a resampling technique especially
  useful for variance and bias estimation. The jackknife pre-dates other
  common resampling methods such as the bootstrap. The jackknife
  estimator of a parameter is found by systematically leaving out each
  observation from a dataset and calculating the estimate and then
  finding the average of these calculations. Given a sample of size n
  $n$, the jackknife estimate is found by aggregating the estimates of
  each $( n − 1 )$-sized sub-sample.


It may also be referred to as leave-one-out cross validation, which isn't exactly the same but very close. 


  Leave-one-out cross validation is K-fold cross validation taken to its
  logical extreme, with K equal to N, the number of data points in the
  set. That means that N separate times, the function approximator is
  trained on all the data except for one point and a prediction is made
  for that point.


Well, that's the name for leaving out a single observation at a time. Strictly speaking, it isn't the name for leaving out each panel unit once. When you resample in way that accounts for the panel or time series structure, that is usually called Block Bootstrapping, in this case a kind of cluster bootstrapping. 

Personally, I would call this block-jacknife or leave-one-block-out cross validation.