The VaR limit is the region in which we trust the numeraire. Outside the VaR boundary, we can't aggregate the data with normal observations, because we can't translate them to a common numeraire. By itself, this is not a new idea in statistics. Standard analysis identifies outliers and analyzes them separately from the rest of the data. Sometimes outliers are data errors or rare exceptions of minor interest. Sometimes they are far more important than variation within normal data. But it is almost never fruitful to combine outliers and ordinary observations in a single analysis.
Wall Street quants took this idea further by identifying the outlier region in advance. As I have said, we were forced to do it by circumstances. No one thought of the approach as a useful way to improve statistics; it was a way to satisfy top-down demands with the tools at hand. Only when we tried to do it did we discover how hard and useful it was. After a few years, we didn't trust any statistical result that didn't have a clear numeraire and validated analysis of situations when the numeraire broke down.
For financial trading applications, the standard process is: