Packet 2: Bonus 15
This statistician names an unbiased estimate of the risk in the normal means problem, which is derived using a lemma named for him that is essentially integration by parts for the Gaussian PDF. For 10 points each:
[10h] With his student Willard James, what statistician developed a shrinkage estimator that shockingly beats the sample mean in dimensions three or more by sharing information across coordinates, even if they are unrelated?
ANSWER: Charles Stein
[10m] The James-Stein estimator is related to a particular OLS regression that lacks one of these terms. These terms correspond to a column of all ones in the design matrix and are often written beta-nought.
ANSWER: intercepts [or y-intercepts; or constants]
[10e] One view of the James-Stein estimator treats it as an empirical Bayes estimator with this distribution chosen to be normal. This distribution on the parameters of interest is updated via the likelihood to obtain the posterior.
ANSWER: prior distribution
<TM, Other Science (Math)> | NAFTA-Packet-2
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 8 | 12.50 | 75% | 13% | 38% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| 2026 NAFTA at Stanford | 01/17/2026 | ✕ | 4 | 7.50 | 50% | 25% | 0% |
| 2026 NAFTA at UBC | 01/17/2026 | ✕ | 2 | 15.00 | 100% | 50% | 0% |
| 2025 NAFTA Online | 02/14/2026 | ✕ | 4 | 7.50 | 50% | 25% | 0% |
| 2026 NAFTA at Vanderbilt | 02/14/2026 | ✕ | 3 | 13.33 | 67% | 67% | 0% |
| 2025 NAFTA at Toronto | 09/13/2025 | ✕ | 4 | 12.50 | 75% | 25% | 25% |
| 2025 NAFTA at Toronto | 09/13/2025 | ✕ | 1 | 10.00 | 0% | 100% | 0% |
| 2025 NAFTA at Maryland | 09/27/2025 | ✓ | 5 | 6.00 | 60% | 0% | 0% |
| 2025 NAFTA at Harvard | 10/04/2025 | ✓ | 3 | 23.33 | 100% | 33% | 100% |
| 2025 NAFTA at Oxford | 10/11/2025 | ✕ | 4 | 10.00 | 50% | 50% | 0% |
| 2025 NAFTA at Chicago | 11/08/2025 | ✕ | 6 | 18.33 | 83% | 67% | 33% |
| 2025 NAFTA at Columbia | 11/08/2025 | ✕ | 5 | 12.00 | 80% | 40% | 0% |
| 2025 NAFTA at Richmond | 12/20/2025 | ✕ | 2 | 10.00 | 50% | 50% | 0% |