Normal Distribution
nothing is called 95% until it has been counted
Concept

Root mean square error — where it appears

The square root of the average squared distance between an estimate and its target, which puts bias and spread into one number. An estimator can be the least biased on a table and the worst on it, because those two components are not comparable until they are squared.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

The estimator has no upper bound on what it costs. What a thinning overlap does to a stabilised inverse-probability estimate of an average effect of 1.0000, over 600 samples of 600 at each of six settings. The spread rises from 0.1965 to 0.8122 and the root mean square error from 0.1964 to 0.9219, so at the thin end the error is very nearly the whole of the quantity being estimated. The lower line is the share of the arm's weighted total the single largest observation owns, averaged over the same draws: 0.69% to 9.78%, and in the worst single draw of the sweep 82.75%. Coverage of the 95% interval goes from 93.7% to 55.5%.

The region with no comparison

A trimmed interval covers the average effect over everybody 90.8% of the time at six hundred rows and 41.0% at nine thousand six hundred, while covering the average effect over the units it kept 94.3% and 96.0% throughout. An interval that gets worse as the sample grows is an interval about something else.

weights · Weighting Either model is enough; neither is not. The bias of three estimators of an average effect of 1.0000, over 600 samples of 600 units with the assignment rule at strength 1, in each of the four cells made by getting each nuisance model right or wrong. The wrong model in both cases is one that omits the second covariate, which the outcome and the assignment both depend on. The outcome model alone is off by 0.8064 whenever it is the wrong one; weighting alone is off by 0.8190 whenever the propensity model is. The augmented estimator built from both is off by -0.0085, -0.0083 and -0.0016 in the three cells where at least one of them is right, and by 0.8118 in the fourth — which is between its two components rather than better than either.

Either model, but not neither

The augmented estimator's bias is −0.0085, −0.0083 and −0.0016 wherever one nuisance model is right, against components off by 0.8064 and 0.8190. One step past the overlap sweep it is the least biased estimator on the table at 0.0857 and the worst on it at 1.9265.

weights · Weighting

Named alongside it

The objects these essays reach for when they reach for this one.

Average treatment effectConfidence intervalHeavy tailInverse-probability weightingPropensity scoreStabilised weightsAugmented estimatorConsistencyDoubly robustEstimandExtreme weightInfluence function

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