Inference Functions and Quadratic Score Tests
Bruce G. Lindsay and Annie Qu
A general expository description is given of the use of quadratic score test statistics as inference functions. This methodology allows one to do efficient estimation and testing in a semiparametric model defined by a set of mean zero estimating function. This inference function is related to a quadratic minimum distance problem. The asymptotic chi-squared properties are shown to be the consequences of asymptotic projection properties. Shortcomings of the asymptotic theory are discussed and a bootstrap method is shown to correct for anticonservative testing behavior.
Key Words Bootstrapping, chi-squared test, Edgeworth expansion, generalized estimating equation, generalized method of moments, likelihood, quadratic inference function, quasilikelihood, semiparametric model.