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This tag is too general; please provide a more specific tag. For questions about the properties of specific estimators, use [estimators] tag instead.
8
votes
3
answers
110
views
Name of mean- or median-like values?
Consider the data points $x_i \in \mathbb R$ for $i=1,\ldots,n$ as well as following definition:
$$\hat x_c := \underset{{r\in \mathbb R}}{\operatorname{argmin}}\sum_i \vert r - x_i \vert^c $$
This de …
1
vote
Name of mean- or median-like values?
This is only a partial answer for $c \in (0,1]$:
A Fréchet mean has the form
$$\Psi(x) = \operatorname{argmin}_r \sum_i d(r, x_i)$$
where $(M,d)$ is a metric space and $x \in M^k$ and $d$ is a metric. …