Sensitivity curve of the Harrell-Davis quantile estimator, Part 2
In the previous post, I have explored the sensitivity curves of the Harrell-Davis quantile estimator on the normal distribution. In this post, I continue the same investigation on the exponential and Cauchy distributions.
The classic Harrell-Davis quantile estimator (see harrell1982) is defined as follows:
where
The standardized sensitivity curve (SC) of an estimator
Thus, the SC shows the standardized change of the estimator value for situation,
when we add a new element
Now let’s explore the SC values for different sample sizes for
Exponential distribution
Cauchy distribution
Conclusion
As we can see, for
References
- [Harrell1982]
Harrell, F.E. and Davis, C.E., 1982. A new distribution-free quantile estimator. Biometrika, 69(3), pp.635-640.
https://doi.org/10.2307/2335999 - [Maronna2019]
Maronna, Ricardo A., R. Douglas Martin, Victor J. Yohai, and Matías Salibián-Barrera. Robust statistics: theory and methods (with R). John Wiley & Sons, 2019.