Question
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)>
Summary
| 2024 Chicago Open | 07/28/2024 | Y | 13 | 10.00 | 92% | 0% | 8% |
Data
| SAYYID QUTB, DRIVING THE LONGEST CAR YOU’VE EVER SEEN THROUGH TAHRIR SQUARE | A Nervy Liberal Nanny Hence | 0 | 0 | 10 | 10 |
| The Empire Bikes Back | Are You There, Chat? It's Me, Margaret | 0 | 0 | 10 | 10 |
| Charlotte's Moderately Successful Team | Galvanized Square Steen and Eco-Friendly Wood Vermeer | 0 | 10 | 10 | 20 |
| Lying on a Mattress at Lou’s Apartment in Pilsen, Chicago | I’ll take a quiet 10 / A handshake of CO (Chicago Open) | 0 | 0 | 0 | 0 |
| LMM's LLM MLM | genAI this, genAI that, have you found your 真爱 yet | 0 | 0 | 10 | 10 |
| Les Missourables | Lisan al-Quib | 0 | 0 | 10 | 10 |
| Berkeley Mafia and the Chicago Boy | NJTRANSit (and anwen, I guess) | 0 | 0 | 10 | 10 |
| AMOGH QUIZ HACK? 英雄联盟 400 PPG 24 TUH | NJTRANSit (and bobby, i guess) | 0 | 0 | 10 | 10 |
| The Jeam Team | Punished "Venom" BHSU | 0 | 0 | 10 | 10 |
| First Cause, First Cause, make me young! | The Dyatlov Passement incident | 0 | 0 | 10 | 10 |
| BHSU B | The Oldest Men in the World | 0 | 0 | 10 | 10 |
| We Need New Names | when you look this good, you don’t have to know anything | 0 | 0 | 10 | 10 |
| Read slowly: A A A A A A A A A A A A A A A Read quickly: A | var merchants | 0 | 0 | 10 | 10 |