Charles Stein - 2025 NAFTA

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; accept biases]

[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 %
30	12.00	67%	47%	7%

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Conversion

Team	Opponent	Part 1	Part 2	Part 3	Total	Parts
A Neg of Beauty is a Joy Forever	C R A B S	0	0	10	10	E
Abbas I founded the Abbasids	UBC A	0	0	10	10	E
Ana Pauker? I hardly know her!	Girls who Just Want to Have Fun + Liam	0	10	10	20	ME
BHSU	Muscle Mass Extinction Event	0	0	10	10	E
Berkeley B	Stanford B	0	0	10	10	E
Chicago !A	Invective Against Swans	10	10	10	30	HME
Dour Straits	No Country for Old Quizzers	0	10	10	20	ME
Execute Order 6 7	(give me an) ANSWER: die for baseball	0	0	0	0
H Charlson's Washed Up Scrubs	Dielectrical Materialism	0	10	0	10	M
Indiana	1000000 Delinquents	0	10	10	20	ME
It's something unpredictable/that in the end is right/please refrain from e-mailing my wife	Copán Seethe	0	0	0	0
Lex	W&L+Friend	0	0	10	10	E
Maybe Ever	St. Marx	0	0	0	0
NYU A	Six Quizbowlers in Search of Owen Minmo	0	10	10	20	ME
Negged Five Times in a Yellow Cab Against the Gottis and Gambinos	NYU B or not NYU B (that is the question)	0	0	0	0
Polish Orthographers Posting Their Łs	David Foster Gromit	0	10	10	20	ME
Quebecois Olga Tokarczuk be like 'freins de jacob interdits'	In the Mood for Transportation Equipment	0	10	10	20	ME
Shipping Down from Ballston	Habitat 67	0	0	10	10	E
Stanford A	Berkeley A	0	10	10	20	ME
Team 7	Constans Constantius and Constantine Jr.	0	0	0	0
Team 8	Not Old! (Old)	0	0	0	0
Tennessee A	Georgia Tech 𓂈𓆉𓃡	0	0	0	0
The Third Time when she was Given to Answer the Hard and the Easy, and Answered Only the Easy	Vacuous Tortoise	0	0	0	0
The Umayyad Caliphate be like REPEAL NAPHTHA	Say It Ain't Zhou	0	10	10	20	ME
The tram is not in service; please use the moving walkway.	Northwestern	10	10	10	30	HME
UBC B	The Unbearable Heaviness of History Players	0	10	10	20	ME
Untitled Keyal Team	The "C" Team	0	10	10	20	ME
Untitled by Alexander McQueen by Premeditated Chaos by Alexander McQueen by Percival Everett	Noah Sheidlower	0	0	10	10	E
WashU	four high school generalists shock natives with fluent stock in Tocharian B	0	10	10	20	ME
[Redacted]	The Worst Trade Deal in the History of Trade Deals	0	0	0	0

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%