Model Checks for Marginal Effects in Proportional Hazard Models (Job Market Paper)
The article considers a specification test of the parametric part of proportional hazard models, which determines the covariate effects. The test is based on a CUSUM process of the martingale residuals. We develop Principal Component Decomposition of the CUSUM residual process, where the components, which are asymptotically independent standard normal variables, provide a basis for different types of tests that specialized in certain directions. The decomposition method we propose extends existing methods, which only work for efficient estimator, in such a way that it is able to accommodate any root-n-consistent estimator. As a result, the omnibus Cramer-von Mises test, which is the squared L2-norm of the CUSUM process, has an orthogonal representation as a weighted sum of all squared components. Smooth tests that based on a few components are also constructed to improve the efficiency. Finite sample performance of the proposed tests is illustrated in the context of a Monte Carlo experiment.
In this paper, we develop new goodness-of-fit tests for the Cox proportional hazard model. We introduce a conditional Principal Component Analysis, which can be applied in general conditional models, however, is demonstrated in the Cox model at present. We decompose the CUSUM process of the martingales, which are implied by the specification, into a weighted sum of asymptotically independent component processes, and construct new tests based on these estimated component processes. The omnibus test, which is a functional of the CUSUM process, downweights the latter components heavily, while our test is based on each component, thus, it outperforms the omnibus test, especially in high-frequency directions. Smooth tests, which are unweighted averages of a few components, are also constructed. The finite sample performance of the tests is illustrated by mean of a Monte Carlo experiment.