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Differentiability properties of the s-mean $$m_ s$$ at $$s=1$$. (English) Zbl 0578.62021
Summary: It is known that the s-means $$m_ s$$ of a probability measure converge for $$s\downarrow 1$$ to a median $$m_ 1$$ called the natural median. For purposes of estimation it is important to know whether $$m_ s$$ is not only continuous but also differentiable at $$s=1$$. We show that the function $$s\to m_ s$$ is indeed differentiable at $$s=1$$ for the case of a unique as well as a non unique median. We also give an explicit formula for the derivative at $$s=1$$.
##### MSC:
 62E99 Statistical distribution theory 62B99 Sufficiency and information
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##### References:
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