Modified Two-stage Least Squares Methods for Estimating Parameters in Nonlinear Regression Models with Correlated Errors - Pukdee, Wannapa (Burapha Science Journal, 2026)
The two-stage least squares method is used to fit nonlinear regression models with correlated errors based on a stationary autoregressive process of order one. This method tends to underestimate the standard error of parameter estimates. Therefore, this paper presents modified two-stage least squares methods by using residuals from the one-way ANOVA model and estimating the correlation coefficient from the conditional least squares procedure to construct a weight matrix. These methods are used to estimate all parameters of nonlinear regression models. A simulation study covers a wide range of correlation levels on the models. The study result shows that the modified two-stage least squares methods can improve the efficient statistical inference since they produce unbiased estimators of parameters and reduce bias in estimating standard errors for parameter estimates.