Robustness
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
Counting targets when the sensors make mistakes
Add up the Euler characteristics of the regions where sensor counts are high and the answer is exactly the number of targets — until one sensor misreads. Each wrong reading is a new piece or a new hole, so the error grows with the number of sensors instead of averaging away. Smooth the readings and count each piece and hole by how long it survives as the threshold is lowered, and the count comes back exactly, with half the readings wrong, at the price of having to know how small a real feature can be.
The best middle when the shape is unknown
The mean is the best estimate of a centre when the data are normal and worthless when they are Cauchy. The median is best for Laplace data and wastes a third of normal data. Between them lie the trimmed means — drop a share from each end, average the rest — and across seven symmetric shapes the best guarantee comes from trimming about 28 per cent from each end, which never does worse than 81 per cent of the best possible. Peter Bickel proved in 1965 that trimming can never cost more than a known factor against the mean, whatever the shape.
Named alongside it
The objects these essays reach for when they reach for this one.
EfficiencyEuler characteristicFisher informationHeavy tailsIntegralMedianPersistenceSensor networkSmoothingTopological invariantTrimmed mean