A Kolmogorov-Smirnov-Type Test for Dependently Double-Truncated Data

With double-truncated lifespans, we test the hypothesis of a parametric distribution family for the lifespan. The typical finding from demography is an instationary behaviour of the life expectancy, and a copula models the resulting weak dependence of lifespan and the age at truncation. Our main example is the Farlie-Gumbel-Morgenststern copula. The test is based on Donsker-class arguments and the functional delta method for empirical processes. The assumptions also allow parametric inference, and proofs slightly simplify due to the compact support of the observations. An algorithm with finitely many operations is given for the computation of the test statistic. Simulations becomes necessary for computing the critical value. With the exponential distribution as an example, and for the application to 55{,}000 German double-truncated enterprise lifespans, the constructed Kolmogorov-Smirnov test rejects clearly an age-homogeneous closure hazard.