  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.
