Inference Functions and Quadratic Score Tests

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 functions. The 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.