Models that are estimated by PROC HPNLMOD can be represented by using the equations
where
is the vector of observed responses
is the nonlinear prediction function of parameters and regressor variables
is the vector of model parameters to be estimated
are the vectors for each of the regressor variables
is the vector of residuals
is the variance of the residuals
In these models, the distribution of the residuals is not specified and the model parameters are estimated using the least squares method. For the standard errors and confidence limits in the “ParameterEstimates” table to apply, the errors are assumed to be homoscedastic, uncorrelated, and have zero mean.