Estimator
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
The median of many small averages
Knowing only that a quantity has a finite spread, the plain average of n samples can be promised to within σ/√(nδ) with confidence 1 − δ, and no better — Chebyshev's bound is tight, and rare large jumps achieve it. Cut the same samples into a dozen blocks, average each block, and take the median of the averages, and the promise improves to within about σ√(log(1/δ)/n). Nothing about the data has been assumed beyond the spread; only the way of combining it has changed.
How many new kinds the next sample will show
Count how many kinds were seen once, twice, three times. Good and Toulmin's alternating sum f₁t − f₂t² + f₃t³ − … then predicts, with no bias at all, how many new kinds a further sample t times as large will reveal. It works perfectly up to t = 1 and is worthless just beyond: past that point the kinds seen most often are multiplied by t to a high power, and the spread of the estimate passes 10⁴⁰ by t = 1.5. Truncating the sum at a random point rescues it, and each fourfold increase in the first sample buys about half a unit more of future.
Named alongside it
The objects these essays reach for when they reach for this one.
VarianceAlternating seriesChebyshev inequalityConfidenceEstimator biasHeavy tailsHoeffding inequalityMedianMedian of meansPoisson approximationPower seriesSampling