On the sensitivity of the overdispersion test in a Weibull model

This paper examines the O(n-1/2) sampling behaviour of the overdispersion test statistic in a Weibull hazard regression model, under the assumption of locally omitted covariates and in the absence of censoring. Although the O(1) sampling distribution is insensitive to this misspecification, by refining the approximation to O(n-1/2) it is shown how the non-centrality parameter of the O(1) asymptotic distribution of the precise score test (i.e., the variance of the omitted term) directly influences the power of the overdispersion test.