Inverted probability loss functions and its applications

Abstract

In most statistical and decision problems, nearly no attention is paid to the precise mathematical form of the loss function. However, the choice of a particular loss function seriously affects the resulting inferences and estimations. This dissertation investigates a general class of loss functions based on the reflection or inversion of a probability density function, Inverted Probability loss function, which was proposed by Spiring and Yeung (1998). We modified the Inverted Probability loss function to be a more generalisation of the original one. To the best of my knowledge and belief, it is the first time to establish such results in the literature. We firmly advocate that there are some novelties in the Inverted Probability Loss Functions and there are even more applications when applying them. In this report, we show the broad coverage and the flexibility of the Loss Functions to make a more robust expected loss.