Application of the Polynomial Maximization Method for Estimating Nonlinear Regression Parameters with Non-gaussian Asymmetric Errors

In the article, an alternative approach to estimating parameters in nonlinear regression models under asymmetric error distributions is examined. A novel approach for adaptive estimation is proposed, which is based on the use of second-order polynomial functions. This enables a straightforward implementation to account for deviations from Gaussian idealization in the form of moments up to the fourth order. It is demonstrated that the overall problem can algorithmically be reduced to the numerical solution of a system of nonlinear stochastic equations. Analytical expressions are obtained, which facilitate the estimation of parameters and the analysis of their asymptotic variance. Statistical modeling using the Monte Carlo method was conducted, and the results indicate that the accuracy of PMM2 estimates is comparable to SLS estimates and significantly so exceeds the accuracy of OLS estimates.