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

See all articles by Chudamani Poudyal

Chudamani Poudyal

University of Wisconsin Milwaukee; University of Central Florida

Vytaras Brazauskas

University of Wisconsin - Milwaukee

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.

Suggested Citation

Poudyal, Chudamani and Brazauskas, Vytaras, Robust Estimation of Loss Models for Truncated and Censored Severity Data (June 1, 2021). Variance 15 (2), 2022., Available at SSRN: https://ssrn.com/abstract=4044121 or http://dx.doi.org/10.2139/ssrn.4044121

Chudamani Poudyal (Contact Author)

University of Wisconsin Milwaukee ( email )

2442 E. Kenwood Blvd.
Milwaukee, WI 53201-0729
United States

University of Central Florida ( email )

Orlando, 32816-1400
United States

Vytaras Brazauskas

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53201
United States

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