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Outlier-resistant confidence intervals for location

An outlier-resistant location confidence interval combines a resistant location estimate with a matched uncertainty procedure and stated coverage assumptions.

Version
v1 · 2026-10-31 · History
Domain-specific #
14547
Domain group
Formal Sciences
Origin domain
Experimental Design & Statistics
Subdomains
Robust Statistics, Interval Estimation → Experimental Design & Statistics

Core Idea

An outlier-resistant confidence interval for location combines a resistant location estimate with a matching uncertainty method, target and nominal confidence level. Resistance of the center does not by itself prove that the interval retains nominal coverage under arbitrary contamination.[1][2]

How would you explain it like I'm…

Not-Fooled Middle Guess

Suppose you want to know the usual height of kids in a class, but one measurement is a silly mistake, like a kid listed as ten feet tall. An outlier-resistant way of guessing the middle doesn't get fooled much by that silly number. Then you also give a range around your guess, made with a method that is supposed to catch the true middle most of the time.

Sturdy Middle With a Range

When you measure a group, you often want the 'location' — a typical middle value. Some numbers might be weird extremes, called outliers, that can pull an ordinary average way off. An outlier-resistant method uses a middle estimate that isn't pulled around much by those extremes. A confidence interval adds a range around that estimate, built by a method designed to capture the true middle a stated share of the time, like 95%. Being resistant to outliers and getting that 95% right are two different things to check.

Robust Location Interval

An outlier-resistant confidence interval for location pairs two things: an estimate of the center (location) designed so that extreme observations have limited influence, and a procedure that produces an interval with a stated nominal confidence level, such as 95%. The target could be a single center or the difference between two centers. The resistant estimator, the uncertainty calculation and their assumptions all have to suit that target. Importantly, resistance and coverage are separate: a center can resist outliers while the interval's coverage still depends on conditions. A 95% level describes how the procedure performs over repeated samples under its assumptions; one interval doesn't prove 95% coverage under every possible kind of contamination.

 

An outlier-resistant confidence interval for location combines a location estimator designed to limit the influence of extreme observations with an uncertainty procedure that yields interval endpoints at a stated nominal confidence level. The inferential target may be a single location parameter or a difference between two locations. The resistant center, the uncertainty calculation and the supporting assumptions must all be appropriate to that target. Crucially, resistance of the point estimate and coverage of the interval are separate properties. A nominal 95% level is a property of a repeated-sampling procedure under its stated conditions; a single realized interval does not demonstrate 95% coverage under every pattern of contamination.

Examples

Iglewicz and Hoaglin calculate a 95% interval of 2211.7 to 2328.1 from eleven gear-tooth strength measurements, using a trimmed center, Winsorized uncertainty and a t reference. They describe a population-mean target; whether a trimmed location has that target depends on assumptions about the population. One interval does not demonstrate repeated-sampling coverage.[1]

Mair and Wilcox report a 20%-trimmed difference of −0.11494 for Spanish and German football teams, with a 95% interval of −0.405 to 0.1751. The estimand is a trimmed-location difference, not automatically an arithmetic-mean difference; inclusion of zero does not prove equality.[2]

Boundaries

A robust scale statistic is not an interval by itself. State the sampling conditions, estimand, endpoint construction and nominal level. Trimming and interval coverage are distinct claims, and other robust interval methods need their own assumptions.

Neighborhood in Abstraction Space

Outlier-resistant confidence intervals for location sits in a moderately populated region (49th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Statistical Learning & Model Failure Modes (44 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-31

References

[1] Boris Iglewicz and David C. Hoaglin, How to Detect and Handle Outliers (American Society for Quality Control, 1993), §4.5, pp. 26–27. https://hwbdocs.env.nm.gov/Los%20Alamos%20National%20Labs/TA%2054/11587.pdf registry ↩a ↩b

[2] Patrick Mair and Rand Wilcox, “Robust Statistical Methods in R Using the WRS2 Package,” Behavior Research Methods 52 (2020), 464–488. https://doi.org/10.3758/s13428-019-01246-w registry ↩a ↩b