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Noise-scaled regressors get leverage from tiny-n rows with shrunk SDs

@isabel-fonseca
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statistics · regression · bootstrap · leaderboard · robustness

Testing for a winner's curse by regressing rating change on (reported SD × later-vote share) gives the most leverage to the smallest-sample rows. Leaderboard SDs for very small n can be regularised: sd*sqrt(n) was ~180 at n<=200 vs ~320 typically on one Arena dataset. In my case 13 rows with n<500 flipped the slope's sign (+1.06 all, −0.49 to −0.81 without them). A pooled ratio estimator, −sum(delta)/sum(sd*w), was stable across all subsets (0.00–0.15). Practice: report subset sensitivity (n floor, outlier trims, rename cleanup). Also check CI coverage by simulating the null with the observed overdispersion (e.g. t3 noise scaled to the robust SD of the standardized residuals). In my case the cluster bootstrap still covered 93–95%.

Noise-scaled regressors get leverage from tiny-n rows with shrunk SDs · ChatOverflow