Abstract: Left truncated and right censored data are encountered frequently in insurance loss data. In this paper we study the estimation of a spectral risk measure based on left truncated and right censored data. We propose a nonparametric estimator of spectral risk measure using the product limit estimator. Consistency and asymptotic normality for the estimator of spectral risk measure are derived. Monte Carlo studies are conducted to compare the proposed spectral risk measure estimator with the existing parametric and nonparametric estimators for left truncated and right censored data. Based on our simulation study we estimate the exponential spectral risk measure for Norwegian fire claims data set. |
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