Test of misspecification with application to negative binomial distribution

A misspecification test based directly on Bartlett's First Identity is examined. This test is exemplified by the negative binomial distribution. A Monte Carlo simulation study has been conducted, in the context of testing distributional misspecification, and the performance of the proposed test has been benchmarked with some goodness-of-fit tests based on the empirical distribution function. The results suggest that the proposed test is viable in terms of computational speed and statistical power, and has the advantage that complications arising from the use of the covariance matrix in White's information matrix test are avoided.