# Robust Estimation of Loss Models for Truncated and Censored Severity Data

arXiv: https://arxiv.org/abs/2202.13000 · HTML: https://mlsanity.com/paper/2202.13000/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2022.

## Built on by (most cited first, 1 of 1)

- [Robust Estimation of the Tail Index of a Single Parameter Pareto Distribution from Grouped Data](https://mlsanity.com/paper/2401.14593/) (2024)

## Abstract (arXiv)

In this paper, we consider robust estimation of claim severity models in insurance, when data are affected by truncation (due to deductibles), censoring (due to policy limits), and scaling (due to coinsurance). In particular, robust estimators based on the methods of trimmed moments (T-estimators) and winsorized moments (W-estimators) are pursued and fully developed. The general definitions of such estimators are formulated and their asymptotic properties are investigated. For illustrative purposes, specific formulas for T- and W-estimators of the tail parameter of a single-parameter Pareto distribution are derived. The practical performance of these estimators is then explored using the well-known Norwegian fire claims data. Our results demonstrate that T- and W-estimators offer a robust and computationally efficient alternative to the likelihood-based inference for models that are affected by deductibles, policy limits, and coinsurance.