Folded medians

In the previous post, we discussed the Gastwirth’s location estimator. In this post, we continue playing with different location estimators. To be more specific, we consider an approach called folded medians. Let \(x = \{ x_1, x_2, \ldots, x_n \}\) be a random sample with order statistics \(\{ x_{(1)}, x_{(2)}, \ldots, x_{(n)} \}\). We build a folded sample using the following form: \[\Bigg\{ \frac{x_{(1)}+x_{(n)}}{2}, \frac{x_{(2)}+x_{(n-1)}}{2}, \ldots, \Bigg\}. \] If \(n\) is odd, the middle ...

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