## The Gauss-Newton Regression

Associated with every nonlinear regression model is a somewhat nonstandard artificial regression which is probably more widely used than any other. Consider the univariate, nonlinear regression model

yt = vt(P) + ut, ut ~ iid(0, о2), t = 1,…, n, (1.2)

where yt is the tth observation on the dependent variable, and в is a ^-vector of parameters to be estimated. The scalar function vt(P) is a nonlinear regression function. It determines the mean value of yt as a function of unknown parameters в and, usually, of explanatory variables, which may include lagged dependent variables. The explanatory variables are not shown explicitly in (1.2), but the t subscript on х((в) reminds us that they are present. The model (1.2) may also be written as

y = x(e) + u, u ~ iid(0, о2I), (1.3)

where y i...

Read More