Associated with every popular nonlinear estimation method is at least one 'artificial' linear regression. We define an artificial regression in terms of three conditions that it must satisfy. Then we show how artificial regressions can be useful for numerical optimization, testing hypotheses, and computing parameter estimates. Several existing artificial regressions are discussed and are shown to satisfy the defining conditions, and a new artificial regression for regression models with heteroskedasticity of unknown form is introduced.
artificial regression LM test specification test Gauss-Newton regression one-step estimation OPG regression double-length regression binary response model