Abstract
Given a location-scale family that is symmetric about its median, the aim is to robustly estimate an effect size defined as the median divided by an interquantile range (IQR), where the quantile is fixed and to be chosen. It is shown that the sample version of this effect size can be variance stabilized, given information about its density at the median and quantiles defining the IQR. Tests for a significant effect size and confidence intervals for this effect size are derived and assessed.
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Acknowledgement
The author thanks both referees and the editor for helpful comments which have greatly improved the manuscript. Also, many thanks to Prof. Hira Lal Koul for his friendship and introducing the author to robust statistics, as well as imparting his immense passion for research.
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Staudte, R. (2014). Inference for the Standardized Median. In: Lahiri, S., Schick, A., SenGupta, A., Sriram, T. (eds) Contemporary Developments in Statistical Theory. Springer Proceedings in Mathematics & Statistics, vol 68. Springer, Cham. https://doi.org/10.1007/978-3-319-02651-0_22
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DOI: https://doi.org/10.1007/978-3-319-02651-0_22
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