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The PIs obtained by minimizing the empirical risk based on the Tube Loss are shown to be of better quality than the PIs obtained by the existing methods in the following sense. First, it yields intervals that attain the prespecified confidence level t $\\in$ (0,1) asymptotically. A theoretical proof of this fact is given. Secondly, the user is allowed to move the interval up or down by controlling the value of a parameter. This helps the user to choose a PI capturing denser regions of the probability distribution of the response variable inside the interval, and thus, sharpening its width. This is shown to be especially useful when the conditional distribution of the response variable is skewed. Further, the Tube Loss based PI estimation method can trade-off between the cover","title":"Tube Loss: A Novel Approach for Prediction Interval Estimation","url":"https://arxiv.org/abs/2412.06853","vendor":"arxiv_cs_ai"},"summary":"arXiv:2412.06853v4 Announce Type: replace-cross \nAbstract: This paper proposes a novel loss function, called 'Tube Loss', for simultaneous estimation of bounds of a Prediction Interval (PI) in the regression setup. The PIs obtained by minimizing the empirical risk based on the Tube Loss are shown to be of better quality than the PIs obtained by the existing methods in the following sense. First, it yields intervals that attain the prespecified confidence level t $\\in$ (0,1) asymptotically. A theoretical proof of this fact is given. Secondly, the user is allowed to move the interval up or down by controlling the value of a parameter. 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