A0247
Title: Testing truncation dependence and goodness-of fit for double-truncated durations
Authors: Anne-Marie Toparkus - Universität Rostock (Germany) [presenting]
Rafael Weissbach - University of Rostock (Germany)
Abstract: When analyzing left- or double-truncated durations, the log-likelihood can be derived from standard results for point processes, and the unobserved sample size can be profiled. Simplifying assumptions include the duration of interest being exponentially distributed or the age at truncation being independent of the duration. Both can be unappealing, so a nonparametric test for the first assumption is derived and a parametric test for the second. The second assumption is problematic when truncation results from data collection within a restricted time period, making the age at truncation equivalent to the date of birth, which conflicts with the progress of life expectancy. The dependence model uses the Gumbel-Barnett copula. Since the hypothesis parameter lies at the boundary, the test statistic's asymptotic distribution is a mixture of a two- and a one-dimensional normal distribution. For the first assumption, a bivariate Kolmogorov-Smirnov goodness-of-fit test is necessary for the additional attribute of age-at-truncation. Firstly, the truncated process' asymptotic behavior is analyzed when the true parameter is known under the null hypothesis. Replacing the unknown true parameter with its estimator alters the test statistic's distribution. The compactness of the truncation region allows for the computation of the test statistic using methods for the bivariate uniform case. Empirical examples include 55,000 lifetimes of German enterprises that ended between 2014 and 2016.
