UC Davis

We develop the generalized score function (GSF), a class of functions that have zero expectation when the distribution under the null hypothesis is correctly specified. Functions of this class can then be used in the generalized score function test (GSFT), which is a goodness-of-fit test for parametric distributions that utilizes the maximum likelihood estimatorand has an asymptotic χ2 distribution. The GSF is then adapted for use with both censored and clustered observations, and methods to estimate the asymptotic covariance matrix are discussed. Simulation studies suggest GSFTs have differing power characteristics depending on the GSF selected, and we focus on developing tests for misspecified baseline hazard functions, misspecified random effect distributions, and nonlinear proportional hazard terms. Two real-data examples are analyzed using the GSFT, with results showing similar conclusions to those drawn by previous studies.