Statistical inference in gamma regression model under left-censored data using R

Abstract

In this paper, we consider the problem of the Gamma regression model under left-censored data with covariates. The method investigated consists of solving left-censored maximum likelihood estimating equations. We show that the resulting estimates are asymptotically normal. A simulation study assesses the proposed parameters’ finite-sample properties and the root mean square error estimates. An application using car insurance data is presented to estimate the covariates coefficients in calculating the provisions for claims to be paid. We examine the effect of the censoring variable on the calculation of provisions. We will employ a machine learning algorithm called Random Forest to show the impact of the presence of the censoring variable. Finally, we address financial risk management that considers the Value at Risk (VaR), the Expected Shortfall (ES), and the backtesting of the VaR.

Journal of Statistical Research 2025, Vol. 59, No. 2, pp. 221-247.