Testing for Lack of Fit in Nonlinear Regression

Abstract

The problem of testing the correctness of a nonlinear response function against unspecified general alternatives is considered. The proposed test statistic is a modification of a nonlinear analogue to the well-known linear regression lack-of-fit test and can be used with or without replication. Asymptotically valid critical points can be obtained from a central $F$-distribution. Also, when the null model is the orthogonal projection of the true model, the test statistic is asymptotically comparable to a random variable with a noncentral $F$-distribution.