Which method is the same idea as OLS but for nonlinear models?

Which method is the same idea as OLS but for nonlinear models?

• A. Nonlinear Least Squares (NLS)
• B. Ordinary Least Squares (OLS)
• C. Maximum Likelihood Estimation (MLE)
• D. Stochastic Gradient Descent

Answer: (A)

The essential idea is extending least-squares fitting to models that are nonlinear in the parameters. Ordinary least squares finds the best fit by minimizing the sum of squared residuals when the relationship is linear in parameters. When the model is nonlinear, you still minimize the same squared residuals, but with a nonlinear function of the parameters, so you use nonlinear least squares. You specify a model y ≈ f(x, beta) where f is nonlinear in beta, and solve for beta to minimize the sum of (y_i − f(x_i, beta))^2. Because the relationship is nonlinear, there’s typically no closed-form solution and iterative algorithms like Gauss-Newton or Levenberg–Marquardt are used to converge to the best-fit parameters. So nonlinear least squares is the natural generalization of OLS to nonlinear models.

The essential idea is extending least-squares fitting to models that are nonlinear in the parameters. Ordinary least squares finds the best fit by minimizing the sum of squared residuals when the relationship is linear in parameters. When the model is nonlinear, you still minimize the same squared residuals, but with a nonlinear function of the parameters, so you use nonlinear least squares. You specify a model y ≈ f(x, beta) where f is nonlinear in beta, and solve for beta to minimize the sum of (y_i − f(x_i, beta))^2. Because the relationship is nonlinear, there’s typically no closed-form solution and iterative algorithms like Gauss-Newton or Levenberg–Marquardt are used to converge to the best-fit parameters. So nonlinear least squares is the natural generalization of OLS to nonlinear models.