Huber's psi of a block's outcomes, standardised by the block's MAD

A bounded representation: each outcome's departure from the block median, in units of the block's median absolute deviation (MAD, scaled by 1.4826 as stats::mad() does, so that it equals the standard deviation for normal outcomes), held within [-k, k]. With k = 1.345, Huber's M-estimate of location is 95 percent as efficient as the mean when the outcomes are normal.

Usage

riposte_huber(y, k = 1.345)

Arguments

y

numeric vector (a single block's outcomes).

k

the cap, in MAD units. Huber's 1.345 by default.

Value

numeric vector the same length as y.

Details

Standardising within block keeps the representation informative whatever the outcome's location and units, and the cap keeps one extreme unit from dominating the block. When more than half of a block's outcomes tie, the MAD is zero; the departures are then divided by the mean absolute departure from the median instead. A block with no spread at all gets zeros.

This is the sixth representation of the default set, following Bowers and Burton, "A More Powerful Test for Randomized Experiments" (working paper), and it reproduces that paper's computation.