Robust Estimation of Loss Models for Truncated and Censored Severity Data
Variance 15 (2), 2022.
33 Pages Posted: 6 Apr 2022 Last revised: 21 Oct 2022
Date Written: June 1, 2021
Abstract
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.
Keywords: Insurance Payments; Loss Models; Robust Estimation; Trimmed and Winsorized Moments; Truncated and Censored Data.
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