The sup-norm (“soup-norm”) of the difference between a CDF named for this adjective and the CDF of the reference distribution is used as the statistic in a Kolmogorov–Smirnov test. For 10 points each:
[10m] Name this adjective that describes the random measure associated to a sample whose distribution function is a step function with jumps at each sample value.
ANSWER: empirical [accept empirical cumulative distribution function or empirical CDF]
[10h] This doubly-eponymous “Fundamental Theorem of Statistics” states that the empirical distribution function converges uniformly to its CDF almost surely, providing the basis for the Kolmogorov–Smirnov test.
ANSWER: Glivenko–Cantelli theorem
[10e] The Glivenko–Cantelli theorem is strengthened by Donsker’s invariance principle, which may be viewed as an extension of this theorem to empirical processes. This theorem states that a rescaled sum of I.I.D. random variables converges to a normal distribution.
ANSWER: central limit theorem [or CLT; accept Lindeberg–Lévy CLT]
<AF/JC, Other Science (Math)>