The phrase "a breakdown point" is correct and usable in written English.
It can be used to refer to a specific moment or situation where something fails or collapses, often in a technical or analytical context.
Example: "The analysis revealed a breakdown point in the system that needed immediate attention to prevent further issues."
Alternatives: "failure point" or "crisis point".
This estimator also has a breakdown point of 29%%.
As an illustration, the median has a breakdown point of 50%%, whereas the mean has a breakdown point of 0%%.
The IQR has a breakdown point of 50%%, which makes it robust to long tails in the distribution while still being a good measure of the dispersion or skewness in the distribution.
The rlms used highly robust M-estimation (via the 'MM' option) with a breakdown point of 0.5 and 95% relative efficiency at the normal.
For now, we note that our use of highly robust linear modelling with a breakdown point of 0.5 [ 36] guards against potential bias in our analyses due to heteroscedasticity.
In this study we propose to include another effective robust estimator, the MM-estimator [ 26], that has been shown to have both a high breakdown point (i.e. the percentage of incorrect observations an estimator can handle before giving an incorrect result) and a high efficiency [ 27, 28], but has not yet been utilised in mapping exercises.
However, the Shamos estimator has only a 29%% breakdown point and 86%% efficiency which is slightly higher than the RC estimator.
To have a normal consistency, we consider the following estimator of α given by hatalpha^{text{IQR}}_{j} = frac{text{IQR} y_{j})}{1.34898}, quad j =1, 2, The estimator (hat alpha ^{text {IQR}}_{j}) is in simple closed-form with a higher breakdown point of 25%%, indicating that it remains consistent even if about 25%percentnt of the data have been contaminated.
Our theoretical results allow us to specify conditions for estimators in our family to achieve a maximum asymptotic breakdown point of 12.
Several of the proposed estimators have a very high breakdown point.
In robust estimation theory, two important concepts characterize the robustness of an estimator: the breakdown point and the influence function.
