Minimizing the expected value of the asymmetric loss function and an inequality for the variance of the loss

ABSTRACT

The coefficients of regression are usually estimated for minimization problems with asymmetric loss functions. In this paper, we rather correct predictions so that the prediction error follows a generalized Gaussian distribution. In our method, we not only minimize the expected value of the asymmetric loss, but also lower the variance of the loss. Predictions usually have errors. Therefore, it is necessary to use predictions in consideration of these errors. Our approach takes into account prediction errors. Furthermore, even if we do not understand the prediction method, which is a possible circumstance in, e.g. deep learning, we can use our method if we know the prediction error distribution and asymmetric loss function. Our method can be applied to procurement of electricity from electricity markets.

Keywords:

• Asymmetric loss function
• gamma function
• generalized Gaussian distribution
• minimizing the expectation value
• risk function

2010 Mathematics Subject Classifications:

• 62A99
• 62E99

Disclosure statement

No potential conflict of interest was reported by the author(s).