A Censored Transformed Model for Proportional Outcomes with Boundary Mass and an Application to Loss Given Default Modeling

• URL: http://arxiv.org/abs/2606.21515v1
• Date: Fri, 19 Jun 2026 15:10:41 GMT
• Title: A Censored Transformed Model for Proportional Outcomes with Boundary Mass and an Application to Loss Given Default Modeling
• Abstract summary: We introduce the zero-one censored transformed normal (ZOCTN) model for proportional responses with potential probability mass at the boundaries 0 and 1.<n>We characterize the transformation parameters establish large-sample properties, and relate the affine-logit specification to broader classes of interior distributions.
• Score: 6.789370732159177
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We introduce the zero-one censored transformed normal (ZOC-TN) model for proportional responses with potential probability mass at the boundaries 0 and 1. The model combines a censored Gaussian variable with a two-parameter affine-logit transformation on the interior (0,1). We characterize the transformation parameters, establish large-sample properties, and relate the affine-logit specification to broader classes of interior distributions. Theoretical and experimental results demonstrate that the proposed model can capture a wider range of qualitative density shapes than several benchmark models while remaining parsimonious, computationally efficient, and numerically stable. Furthermore, the ZOC-TN model can be extended (i) to account for nonlinearities and interactions in a tree-boosting machine learning framework and (ii) to explicitly model residual spatio-temporal variability. We apply the ZOC-TN model to loss given default (LGD) modeling for a large dataset of U.S. residential mortgages and compare it to multiple benchmark models. We find that a tree-boosted ZOC-TN model with a spatio-temporal frailty Gaussian process delivers the strongest out-of-sample performance, indicating that mortgage losses are shaped by nonlinear covariate effects and by unaccounted-for space-time variation.

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