Inequality for the variance of an asymmetric loss

12/31/2022

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by   Naoya Yamaguchi, et al.

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We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.