  Principal component analysis has been used to reduce dimensionality of
datasets for a long time. In this paper, we will demonstrate that in mode
detection the components of smallest variance, the pettiest components, are
more important. We prove that when the data follows a multivariate normal
distribution, by implementing "pettiest component analysis" when the data is
normally distributed, we obtain boxes of optimal size in the sense that their
size is minimal over all possible boxes with the same number of dimensions and
given probability. We illustrate our result with a simulation revealing that
pettiest component analysis works better than its competitors.
