  Big Data has become an ever more commonplace setting that is encountered by
data analysts. In the Big Data setting, analysts are faced with very large
numbers of observations as well as data that arrive as a stream, both of which
are phenomena that many traditional statistical techniques are unable to
contend with. Unfortunately, many of these traditional techniques are useful
and cannot be discarded. One such technique is the Kolmogorov-Smirnov (KS) test
for goodness-of-fit (GoF). A Big Data and stream-appropriate KS-type test is
derived via the chunked-and-averaged (CA) estimator paradigm. The new test is
termed the CAKS GoF test. The CAKS test statistic is proved to be
asymptotically normal, allowing for the large sample testing of GoF.
Furthermore, theoretical results demonstrate that the CAKS test is consistent
against both fixed alternatives, where the null and the true data generating
distribution are a fixed distance apart, and alternatives that approach the
null at a slow enough rate. Numerical results demonstrate that the CAKS test is
effective in identifying deviation in the distribution with respect to changes
in mean, variance, and shape. Furthermore, it is found that the CAKS test is
faster than the KS test, for large numbers of observation, and can be applied
to sample sizes of 10^{9} and beyond.
